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Differential geometrical methods in mathematical physics : proceedings of the conference held at Aix-En-Provence, September 3-7, 1979 and Salamanca, September 10-14 1979 / / edited by P. L. Garcia, A. Perez-Rendon, J. M. Souriau
| Differential geometrical methods in mathematical physics : proceedings of the conference held at Aix-En-Provence, September 3-7, 1979 and Salamanca, September 10-14 1979 / / edited by P. L. Garcia, A. Perez-Rendon, J. M. Souriau |
| Edizione | [1st ed. 1980.] |
| Pubbl/distr/stampa | Berlin ; ; Heidelberg : , : Springer-Verlag, , [1980] |
| Descrizione fisica | 1 online resource (XIV, 542 p.) |
| Disciplina | 516.36 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Geometry, Differential
Mathematical physics |
| ISBN | 3-540-38405-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Configuration spaces of identical particles -- The geometrical meaning and globalization of the Hamilton-Jacobi method -- The Euler-Lagrange resolution -- On the prequantum description of spinning particles in an external gauge field -- Classical action, the wu-yang phase factor and prequantization -- Groupes differentiels -- Representations that remain irreducible on parabolic subgroups -- Non-positive polarizations and half-forms -- Connections on symplectic manifolds and geometric quantization -- Geometric aspects of the feynman integral -- Relativistic quantum theory in complex spacetime -- Existence et equivalence de deformations associatives associees a une variete symplectique -- A new symplectic structure of field theory -- Conformal structures and connections -- Equilibrium configurations of fluids in general relativity -- Quaternionic and supersymmetric ? — models -- Supergravity as the gauge theory of supersymmetry -- Hypergravities -- Preface -- Preface -- Morse theory and the yang-mills equations -- Reduction of the yang mills equations -- Tangent structure of Yang-Mills equations and hodge theory -- Classification of gauge fields and group representations -- Gauge asthenodynamics (SU(2/1)) (classical discussion) -- Spinors on fibre bundles and their use in invariant models -- Glueing broken symmetries together -- Deformations and quantization -- Stability theory and quantization -- Presymplectic manifolds and the quantization of relativistic particle systems -- Geometric quantisation for singular lagrangians -- Electron scattering on magnetic monopoles -- The metaplectic representation, weyl operators and spectral theory -- Supergravity: A unique self-interacting theory -- General relativity as a gauge theory -- On a purely affine formulation of general relativity -- A fibre bundle description of coupled gravitational and gauge fields -- Homogenous symplectic formulation of field dynamics and the poincaré-cartan form -- Spectral sequences and the inverse problem of the calculus of variations -- Geodesic fields in the calculus of variations of multiple integrals depending on derivatives of higher order -- Separability structures on riemannian manifolds. |
| Record Nr. | UNISA-996466641403316 |
| Berlin ; ; Heidelberg : , : Springer-Verlag, , [1980] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Differential geometrical methods in mathematical physics II : proceedings, University of Bonn, July 13-16, 1977 / / K. Bleuler, H. R. Petry, A. Reetz
| Differential geometrical methods in mathematical physics II : proceedings, University of Bonn, July 13-16, 1977 / / K. Bleuler, H. R. Petry, A. Reetz |
| Autore | Bleuler Konrad <1912-> |
| Edizione | [1st ed. 1978.] |
| Pubbl/distr/stampa | Berlin : , : Springer, , [1978] |
| Descrizione fisica | 1 online resource (VI, 626 p.) |
| Disciplina | 516.36 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Geometry, Differential
Mathematical physics |
| ISBN | 3-540-35721-1 |
| Classificazione |
00Bxx
53-06 55-06 57-06 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | On the role of field theories in our physical conception of geometry -- Characteristic classes and solutions of gauge theories -- Classification of classical yang-mills fields -- Bundle representations and their applications -- to gauge theory -- The use of exterior forms in field theory -- Electromagnetic fields on manifolds: Betti numbers, monopoles and strings, minimal coupling -- Gravity is the gauge theory of the parallel — transport modification of the poincare group -- On the lifting of structure groups -- On the non-uniqueness of spin structure in superconductivity -- Conformal invariance in field theory -- Geometric quantization and the WKB approximation -- Some properties of half-forms -- On some approach to geometric quantization -- Representations associated to minimal co-adjoint orrits -- On the Schrödinger equation given by geometric quantisation -- Application of geometric quantization in quantum mechanics -- Thermodynamique et Geometrie -- Some preliminary remarks on the formal variational calculus of gel'fand and dikii -- Reducibility of the symplectic structure of minimal interactions -- Ambiguities in canonical transformations of classical systems and the spectra of quantum observables -- Quantum field theory in curved space-times a general mathematical framework -- On functional integrals in curved spacetime -- Observables for quantum fields on curved background -- Quantization of fields on a curved background -- Supergravity -- Representations of classical lie superalgebras. |
| Record Nr. | UNISA-996466759303316 |
Bleuler Konrad <1912->
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| Berlin : , : Springer, , [1978] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Differential geometry : manifolds, curves, and surfaces / Marcel Berger, Bernard Gostiaux ; translated from the French by Silvio Levy
| Differential geometry : manifolds, curves, and surfaces / Marcel Berger, Bernard Gostiaux ; translated from the French by Silvio Levy |
| Autore | Berger, Marcel |
| Pubbl/distr/stampa | New York : Springer-Verlag, c1988 |
| Descrizione fisica | xii, 474 p. : ill. ; 25 cm |
| Disciplina | 516.36 |
| Altri autori (Persone) | Gostiaux, Bernardauthor |
| Collana | Graduate texts in mathematics, 0072-5285 ; 115 |
| Soggetto topico | Geometry, Differential |
| ISBN | 0387966269 |
| Classificazione |
AMS 53-01
LC QA641 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNISALENTO-991001953319707536 |
|
Berger, Marcel
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| New York : Springer-Verlag, c1988 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Differential Geometry [[electronic resource] ] : Theory and Applications
| Differential Geometry [[electronic resource] ] : Theory and Applications |
| Autore | Ciarlet Philippe G |
| Pubbl/distr/stampa | Singapore, : World Scientific Publishing Company, 2008 |
| Descrizione fisica | 1 online resource (300 p.) |
| Disciplina | 516.36 |
| Altri autori (Persone) | LiTa-Tsien |
| Collana |
Series in Contemporary Applied Mathematics
Series in contemporary applied mathematics |
| Soggetto topico | Geometry, Differential |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-91177-1
9786611911775 981-277-147-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; Philippe G. Ciarlet: An Introduction to Differential Geometry in R3; Introduction; 1 Three-dimensional differential geometry Outline; 1.1 Curvilinear coordinates; 1.2 Metric tensor; 1.3 Volumes, areas, and lengths in curvilinear coordinates; 1.4 Covariant derivatives of a vector field; 1.5 Necessary conditions satisfied by the metric tensor; the Riemann curvature tensor; 1.6 Existence of an immersion defined on an open set in R3 with a prescribed metric tensor; 1.7 Uniqueness up to isometries of immersions with the same metric tensor
1.8 Continuity of an immersion as a function of its metric tensor2 Differential geometry of surfaces Out line; 2.1 Curvilinear coordinates on a surface; 2.2 First fundamental form; 2.3 Areas and lengths on a surface; 2.4 Second fundamental form; curvature on a surface; 2.5 Principal curvatures; Gaussian curvature; 2.6 Covariant derivatives of a vector field defined on a surface; the Gauss and Weingarten formulas; 2.7 Necessary conditions satisfied by the first and second fundamental forms: the Gauss and Codazzi-Mainardi equations; Gauss' Theorema Ggregium 2.8 Existence of a surface with prescribed first and second fundamental forms2.9 Uniqueness up to proper isometries of surfaces with the same fundamental forms; 2.10 Continuity of a surface as a function of its fundamental forms; References; Philzppe G. Ciarlet, Cristinel Mardare: An Introduction to Shell Theory; Introduction; 1 Three-dimensional theory Outline; 1.1 Notation, definitions, and some basic formulas; 1.2 Equations of equilibrium; 1.3 Constitutive equations of elastic materials; 1.4 The equations of nonlinear and linearized three-dimensional elasticity 1.5 A fundamental lemma of J.L. Lions1.6 Existence theory in linearized three-dimensional elasticity; 1.7 Existence theory in nonlinear three-dimensional elasticity by the implicit function theorem; 1.8 Existence theory in nonlinear three-dimensional elasticity by the minimization of energy (John Ball's approach); 2 Two-dimensional theory Outline; 2.1 A quick review of the differential geometry of surfaces in R3; 2.2 Geometry of a shell; 2.3 The three-dimensional shell equations; 2.4 The two-dimensional approach to shell theory; 2.5 Nonlinear shell models obtained by r-convergence 2.6 Linear shell models obtained by asymptotic analysis2.7 The nonlinear Koiter shell model; 2.8 The linear Koiter shell model; 2.9 Korn's inequalities on a surface; 2.10 Existence, uniqueness, and regularity of the solution to the linear Koiter shell model; References; Dominique Chapelle: Some New Results and Current Challenges in the Finite Element Analysis of Shells; 1 Introduction; 2 Two families of shell finite elements; 2.1 Discretizations of classical shell models; 2.2 General shell elements; 3 Computational reliability issues for thin shells; 3.1 Asymptotic behaviours of shell models 3.2 Asymptotic reliability of shell finite elements |
| Record Nr. | UNINA-9910453354403321 |
|
Ciarlet Philippe G
|
||
| Singapore, : World Scientific Publishing Company, 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential Geometry [[electronic resource] ] : Theory and Applications
| Differential Geometry [[electronic resource] ] : Theory and Applications |
| Autore | Ciarlet Philippe G |
| Pubbl/distr/stampa | Singapore, : World Scientific Publishing Company, 2008 |
| Descrizione fisica | 1 online resource (300 p.) |
| Disciplina | 516.36 |
| Altri autori (Persone) | LiTa-Tsien |
| Collana |
Series in Contemporary Applied Mathematics
Series in contemporary applied mathematics |
| Soggetto topico | Geometry, Differential |
| ISBN |
1-281-91177-1
9786611911775 981-277-147-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; Philippe G. Ciarlet: An Introduction to Differential Geometry in R3; Introduction; 1 Three-dimensional differential geometry Outline; 1.1 Curvilinear coordinates; 1.2 Metric tensor; 1.3 Volumes, areas, and lengths in curvilinear coordinates; 1.4 Covariant derivatives of a vector field; 1.5 Necessary conditions satisfied by the metric tensor; the Riemann curvature tensor; 1.6 Existence of an immersion defined on an open set in R3 with a prescribed metric tensor; 1.7 Uniqueness up to isometries of immersions with the same metric tensor
1.8 Continuity of an immersion as a function of its metric tensor2 Differential geometry of surfaces Out line; 2.1 Curvilinear coordinates on a surface; 2.2 First fundamental form; 2.3 Areas and lengths on a surface; 2.4 Second fundamental form; curvature on a surface; 2.5 Principal curvatures; Gaussian curvature; 2.6 Covariant derivatives of a vector field defined on a surface; the Gauss and Weingarten formulas; 2.7 Necessary conditions satisfied by the first and second fundamental forms: the Gauss and Codazzi-Mainardi equations; Gauss' Theorema Ggregium 2.8 Existence of a surface with prescribed first and second fundamental forms2.9 Uniqueness up to proper isometries of surfaces with the same fundamental forms; 2.10 Continuity of a surface as a function of its fundamental forms; References; Philzppe G. Ciarlet, Cristinel Mardare: An Introduction to Shell Theory; Introduction; 1 Three-dimensional theory Outline; 1.1 Notation, definitions, and some basic formulas; 1.2 Equations of equilibrium; 1.3 Constitutive equations of elastic materials; 1.4 The equations of nonlinear and linearized three-dimensional elasticity 1.5 A fundamental lemma of J.L. Lions1.6 Existence theory in linearized three-dimensional elasticity; 1.7 Existence theory in nonlinear three-dimensional elasticity by the implicit function theorem; 1.8 Existence theory in nonlinear three-dimensional elasticity by the minimization of energy (John Ball's approach); 2 Two-dimensional theory Outline; 2.1 A quick review of the differential geometry of surfaces in R3; 2.2 Geometry of a shell; 2.3 The three-dimensional shell equations; 2.4 The two-dimensional approach to shell theory; 2.5 Nonlinear shell models obtained by r-convergence 2.6 Linear shell models obtained by asymptotic analysis2.7 The nonlinear Koiter shell model; 2.8 The linear Koiter shell model; 2.9 Korn's inequalities on a surface; 2.10 Existence, uniqueness, and regularity of the solution to the linear Koiter shell model; References; Dominique Chapelle: Some New Results and Current Challenges in the Finite Element Analysis of Shells; 1 Introduction; 2 Two families of shell finite elements; 2.1 Discretizations of classical shell models; 2.2 General shell elements; 3 Computational reliability issues for thin shells; 3.1 Asymptotic behaviours of shell models 3.2 Asymptotic reliability of shell finite elements |
| Record Nr. | UNINA-9910782599003321 |
|
Ciarlet Philippe G
|
||
| Singapore, : World Scientific Publishing Company, 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential Geometry [[electronic resource] ] : Theory and Applications
| Differential Geometry [[electronic resource] ] : Theory and Applications |
| Autore | Ciarlet Philippe G |
| Pubbl/distr/stampa | Singapore, : World Scientific Publishing Company, 2008 |
| Descrizione fisica | 1 online resource (300 p.) |
| Disciplina | 516.36 |
| Altri autori (Persone) | LiTa-Tsien |
| Collana |
Series in Contemporary Applied Mathematics
Series in contemporary applied mathematics |
| Soggetto topico | Geometry, Differential |
| ISBN |
1-281-91177-1
9786611911775 981-277-147-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; Philippe G. Ciarlet: An Introduction to Differential Geometry in R3; Introduction; 1 Three-dimensional differential geometry Outline; 1.1 Curvilinear coordinates; 1.2 Metric tensor; 1.3 Volumes, areas, and lengths in curvilinear coordinates; 1.4 Covariant derivatives of a vector field; 1.5 Necessary conditions satisfied by the metric tensor; the Riemann curvature tensor; 1.6 Existence of an immersion defined on an open set in R3 with a prescribed metric tensor; 1.7 Uniqueness up to isometries of immersions with the same metric tensor
1.8 Continuity of an immersion as a function of its metric tensor2 Differential geometry of surfaces Out line; 2.1 Curvilinear coordinates on a surface; 2.2 First fundamental form; 2.3 Areas and lengths on a surface; 2.4 Second fundamental form; curvature on a surface; 2.5 Principal curvatures; Gaussian curvature; 2.6 Covariant derivatives of a vector field defined on a surface; the Gauss and Weingarten formulas; 2.7 Necessary conditions satisfied by the first and second fundamental forms: the Gauss and Codazzi-Mainardi equations; Gauss' Theorema Ggregium 2.8 Existence of a surface with prescribed first and second fundamental forms2.9 Uniqueness up to proper isometries of surfaces with the same fundamental forms; 2.10 Continuity of a surface as a function of its fundamental forms; References; Philzppe G. Ciarlet, Cristinel Mardare: An Introduction to Shell Theory; Introduction; 1 Three-dimensional theory Outline; 1.1 Notation, definitions, and some basic formulas; 1.2 Equations of equilibrium; 1.3 Constitutive equations of elastic materials; 1.4 The equations of nonlinear and linearized three-dimensional elasticity 1.5 A fundamental lemma of J.L. Lions1.6 Existence theory in linearized three-dimensional elasticity; 1.7 Existence theory in nonlinear three-dimensional elasticity by the implicit function theorem; 1.8 Existence theory in nonlinear three-dimensional elasticity by the minimization of energy (John Ball's approach); 2 Two-dimensional theory Outline; 2.1 A quick review of the differential geometry of surfaces in R3; 2.2 Geometry of a shell; 2.3 The three-dimensional shell equations; 2.4 The two-dimensional approach to shell theory; 2.5 Nonlinear shell models obtained by r-convergence 2.6 Linear shell models obtained by asymptotic analysis2.7 The nonlinear Koiter shell model; 2.8 The linear Koiter shell model; 2.9 Korn's inequalities on a surface; 2.10 Existence, uniqueness, and regularity of the solution to the linear Koiter shell model; References; Dominique Chapelle: Some New Results and Current Challenges in the Finite Element Analysis of Shells; 1 Introduction; 2 Two families of shell finite elements; 2.1 Discretizations of classical shell models; 2.2 General shell elements; 3 Computational reliability issues for thin shells; 3.1 Asymptotic behaviours of shell models 3.2 Asymptotic reliability of shell finite elements |
| Record Nr. | UNINA-9910827585103321 |
|
Ciarlet Philippe G
|
||
| Singapore, : World Scientific Publishing Company, 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential geometry : curves - surfaces - manifolds / Wolfgang Kühnel ; translated by Bruce Hunt
| Differential geometry : curves - surfaces - manifolds / Wolfgang Kühnel ; translated by Bruce Hunt |
| Autore | Kühnel, Wolfgang |
| Pubbl/distr/stampa | Providüence, R. I. : American Mathematical Society, c2002 |
| Descrizione fisica | x, 358 p. : ill. ; 22 cm |
| Disciplina | 516.36 |
| Collana | Student mathematical library, 1520-9121 ; 16 |
| Soggetto topico | Geometry, Differential |
| ISBN | 0821826565 |
| Classificazione |
AMS 53-01
LC QA641.K9613 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNISALENTO-991002640919707536 |
|
Kühnel, Wolfgang
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| Providüence, R. I. : American Mathematical Society, c2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Differential geometry / / Victor V. Prasolov
| Differential geometry / / Victor V. Prasolov |
| Autore | Prasolov V. V (Viktor Vasilʹevich) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (278 pages) |
| Disciplina | 516.36 |
| Collana | Moscow Lectures |
| Soggetto topico |
Geometry, Differential
Geometria diferencial |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-92249-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Basic Notation -- Contents -- 1 Curves in the Plane -- 1.1 Curvature and the Frenet-Serret Formulas -- 1.2 Osculating Circles -- 1.3 The Total Curvature of a Closed Plane Curve -- 1.4 Four-Vertex Theorem -- 1.5 The Natural Equation of a Plane Curve -- 1.6 Whitney-Graustein Theorem -- 1.7 Tube Area and Steiner's Formula -- 1.8 The Envelope of a Family of Curves -- 1.9 Evolute and Involute -- 1.10 Isoperimetric Inequality -- 1.11 Affine Unimodular Differential Geometry -- 1.12 Projective Differential Geometry -- 1.13 The Measure of the Set of Lines Intersecting a Given Curve -- 1.14 Solutions of Problems -- 2 Curves in Space -- 2.1 Curvature and Torsion: The Frenet-Serret Formulas -- 2.2 An Osculating Plane -- 2.3 Total Curvature of a Closed Curve -- 2.4 Bertrand Curves -- 2.5 The Frenet-Serret Formulas in Many-Dimensional Space -- 2.6 Solutions of Problems -- 3 Surfaces in Space -- 3.1 The First Quadratic Form -- 3.2 The Darboux Frame of a Curve on a Surface -- 3.3 Geodesics -- 3.4 The Second Quadratic Form -- 3.5 Gaussian Curvature -- 3.6 Gaussian Curvature and Differential Forms -- 3.7 The Gauss-Bonnet Theorem -- 3.8 Christoffel Symbols -- 3.9 The Spherical Gauss Map -- 3.10 The Geodesic Equation -- 3.11 Parallel Transport Along a Curve -- 3.12 Covariant Differentiation -- 3.13 The Gauss and Codazzi-Mainardi Equations -- 3.14 Riemann Curvature Tensor -- 3.15 Exponential Map -- 3.16 Lines of Curvature and Asymptotic Lines -- 3.17 Minimal Surfaces -- 3.18 The First Variation Formula -- 3.19 The Second Variation Formula -- 3.20 Jacobi Vector Fields and Conjugate Points -- 3.21 Jacobi's Theorem on a Normal Spherical Image -- 3.22 Surfaces of Constant Gaussian Curvature -- 3.23 Rigidity (Unbendability) of the Sphere -- 3.24 Convex Surfaces: Hadamard's Theorem -- 3.25 The Laplace-Beltrami Operator -- 3.26 Solutions of Problems.
4 Hypersurfaces in Rn+1: Connections -- 4.1 The Weingarten Operator -- 4.2 Connections on Hypersurfaces -- 4.3 Geodesics on Hypersurfaces -- 4.4 Convex Hypersurfaces -- 4.5 Minimal Hypersurfaces -- 4.6 Steiner's Formula -- 4.7 Connections on Vector Bundles -- 4.8 Geodesics -- 4.9 The Curvature Tensor and the Torsion Tensor -- 4.10 The Curvature Matrix of a Connection -- 4.11 Solutions of Problems -- 5 Riemannian Manifolds -- 5.1 Levi-Cività Connection -- 5.2 Symmetries of the Riemann Tensor -- 5.3 Geodesics on Riemannian Manifolds -- 5.4 The Hopf-Rinow Theorem -- 5.5 The Existence of Complete Riemannian Metrics -- 5.6 Covariant Differentiation of Tensors -- 5.7 Sectional Curvature -- 5.8 Ricci Tensor -- 5.9 Riemannian Submanifolds -- 5.10 Totally Geodesic Submanifolds -- 5.11 Jacobi Fields and Conjugate Points -- 5.12 Product of Riemannian Manifolds -- 5.13 Holonomy -- 5.14 Commutator and Curvature -- 5.15 Solutions of Problems -- 6 Lie Groups -- 6.1 Lie Groups and Algebras -- 6.2 Adjoint Representation and the Killing Form -- 6.3 Connections and Metrics on Lie Groups -- 6.4 Maurer-Cartan Equations -- 6.5 Invariant Integration on a Compact Lie Group -- 6.6 Lie Derivative -- 6.7 Infinitesimal Isometries -- 6.8 Homogeneous Spaces -- 6.9 Symmetric Spaces -- 6.10 Solutions of Problems -- 7 Comparison Theorems, Curvature and Topology, and Laplacian -- 7.1 The Simplest Comparison Theorems -- 7.2 The Cartan-Hadamard Theorem -- 7.3 Manifolds of Positive Curvature -- 7.4 Manifolds of Constant Curvature -- 7.5 Laplace Operator -- 7.6 Solutions of Problems -- 8 Appendix -- 8.1 Differentiation of Determinants -- 8.2 Jacobi Identity for the Commutator of Vector Fields -- 8.3 The Differential of a 1-Form -- Bibliography -- Index. |
| Record Nr. | UNISA-996466418903316 |
|
Prasolov V. V (Viktor Vasilʹevich)
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Differential geometry / / Victor V. Prasolov
| Differential geometry / / Victor V. Prasolov |
| Autore | Prasolov V. V (Viktor Vasilʹevich) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (278 pages) |
| Disciplina | 516.36 |
| Collana | Moscow Lectures |
| Soggetto topico |
Geometry, Differential
Geometria diferencial |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-92249-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Basic Notation -- Contents -- 1 Curves in the Plane -- 1.1 Curvature and the Frenet-Serret Formulas -- 1.2 Osculating Circles -- 1.3 The Total Curvature of a Closed Plane Curve -- 1.4 Four-Vertex Theorem -- 1.5 The Natural Equation of a Plane Curve -- 1.6 Whitney-Graustein Theorem -- 1.7 Tube Area and Steiner's Formula -- 1.8 The Envelope of a Family of Curves -- 1.9 Evolute and Involute -- 1.10 Isoperimetric Inequality -- 1.11 Affine Unimodular Differential Geometry -- 1.12 Projective Differential Geometry -- 1.13 The Measure of the Set of Lines Intersecting a Given Curve -- 1.14 Solutions of Problems -- 2 Curves in Space -- 2.1 Curvature and Torsion: The Frenet-Serret Formulas -- 2.2 An Osculating Plane -- 2.3 Total Curvature of a Closed Curve -- 2.4 Bertrand Curves -- 2.5 The Frenet-Serret Formulas in Many-Dimensional Space -- 2.6 Solutions of Problems -- 3 Surfaces in Space -- 3.1 The First Quadratic Form -- 3.2 The Darboux Frame of a Curve on a Surface -- 3.3 Geodesics -- 3.4 The Second Quadratic Form -- 3.5 Gaussian Curvature -- 3.6 Gaussian Curvature and Differential Forms -- 3.7 The Gauss-Bonnet Theorem -- 3.8 Christoffel Symbols -- 3.9 The Spherical Gauss Map -- 3.10 The Geodesic Equation -- 3.11 Parallel Transport Along a Curve -- 3.12 Covariant Differentiation -- 3.13 The Gauss and Codazzi-Mainardi Equations -- 3.14 Riemann Curvature Tensor -- 3.15 Exponential Map -- 3.16 Lines of Curvature and Asymptotic Lines -- 3.17 Minimal Surfaces -- 3.18 The First Variation Formula -- 3.19 The Second Variation Formula -- 3.20 Jacobi Vector Fields and Conjugate Points -- 3.21 Jacobi's Theorem on a Normal Spherical Image -- 3.22 Surfaces of Constant Gaussian Curvature -- 3.23 Rigidity (Unbendability) of the Sphere -- 3.24 Convex Surfaces: Hadamard's Theorem -- 3.25 The Laplace-Beltrami Operator -- 3.26 Solutions of Problems.
4 Hypersurfaces in Rn+1: Connections -- 4.1 The Weingarten Operator -- 4.2 Connections on Hypersurfaces -- 4.3 Geodesics on Hypersurfaces -- 4.4 Convex Hypersurfaces -- 4.5 Minimal Hypersurfaces -- 4.6 Steiner's Formula -- 4.7 Connections on Vector Bundles -- 4.8 Geodesics -- 4.9 The Curvature Tensor and the Torsion Tensor -- 4.10 The Curvature Matrix of a Connection -- 4.11 Solutions of Problems -- 5 Riemannian Manifolds -- 5.1 Levi-Cività Connection -- 5.2 Symmetries of the Riemann Tensor -- 5.3 Geodesics on Riemannian Manifolds -- 5.4 The Hopf-Rinow Theorem -- 5.5 The Existence of Complete Riemannian Metrics -- 5.6 Covariant Differentiation of Tensors -- 5.7 Sectional Curvature -- 5.8 Ricci Tensor -- 5.9 Riemannian Submanifolds -- 5.10 Totally Geodesic Submanifolds -- 5.11 Jacobi Fields and Conjugate Points -- 5.12 Product of Riemannian Manifolds -- 5.13 Holonomy -- 5.14 Commutator and Curvature -- 5.15 Solutions of Problems -- 6 Lie Groups -- 6.1 Lie Groups and Algebras -- 6.2 Adjoint Representation and the Killing Form -- 6.3 Connections and Metrics on Lie Groups -- 6.4 Maurer-Cartan Equations -- 6.5 Invariant Integration on a Compact Lie Group -- 6.6 Lie Derivative -- 6.7 Infinitesimal Isometries -- 6.8 Homogeneous Spaces -- 6.9 Symmetric Spaces -- 6.10 Solutions of Problems -- 7 Comparison Theorems, Curvature and Topology, and Laplacian -- 7.1 The Simplest Comparison Theorems -- 7.2 The Cartan-Hadamard Theorem -- 7.3 Manifolds of Positive Curvature -- 7.4 Manifolds of Constant Curvature -- 7.5 Laplace Operator -- 7.6 Solutions of Problems -- 8 Appendix -- 8.1 Differentiation of Determinants -- 8.2 Jacobi Identity for the Commutator of Vector Fields -- 8.3 The Differential of a 1-Form -- Bibliography -- Index. |
| Record Nr. | UNINA-9910544876403321 |
|
Prasolov V. V (Viktor Vasilʹevich)
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential geometry [[electronic resource] /] / [by] J. J. Stoker
| Differential geometry [[electronic resource] /] / [by] J. J. Stoker |
| Autore | Stoker J. J (James Johnston), <1905-> |
| Pubbl/distr/stampa | New York, : Wiley-Interscience, 1989, c1969 |
| Descrizione fisica | 1 online resource (428 p.) |
| Disciplina |
516
516.7 |
| Collana | Pure and applied mathematics, v. 20 |
| Soggetto topico |
Geometry, Differential
Manifolds (Mathematics) |
| ISBN |
1-283-27398-5
9786613273987 1-118-16546-2 1-118-16547-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Differential Geometry; CONTENTS; Chapter I Operations with Vectors; 1. The vector notation; 2. Addition of vectors; 3. Multiplication by scalars; 4. Representation of a vector by means of linearly independent vectors; 5. Scalar product; 6. Vector product; 7. Scalar triple product; 8. Invariance under orthogonal transformations; 9. Vector calculus; Chapter II Plane Curves; 1. Introduction; 2. Regular curves; 3. Change of parameters; 4. Invariance under changes of parameter; 5. Tangent lines and tangent vectors of a curve; 6. Orientation of a curve; 7. Length of a curve
1. Regular curves2. Length of a curve; 3. Curvature of space curves; 4. Principal normal and osculating plane; 5. Binormal vector; 6. Torsion τ of a space curve; 7. The Frenet equations for space curves; 8. Rigid body motions and the rotation vector; 9. The Darboux vector; 10. Formulas for κ and τ; 11. The sign of τ; 12. Canonical representation of a curve; 13. Existence and uniqueness of a space curve for given κ (S), τ (S); 14. What about κ = 0?; 15. Another way to define space curves; 16. Some special curves; Chapter IV The Basic Elements of Surface Theory 1. Regular surfaces in Euclidean space2. Change of parameters; 3. Curvilinear coordinate curves on a surface; 4. Tangent plane and normal vector; 5. Length of curves and first fundamental form; 6. Invariance of the first fundamental form; 7. Angle measurement on surfaces; 8. Area of a surface; 9. A few examples; 10. Second fundamental form of a surface; 11. Osculating paraboloid; 12. Curvature of curves on a surface; 13. Principal directions and principal curvatures; 14. Mean curvature H and Gaussian curvature K; 15. Another definition of the Gaussian curvature K; 16. Lines of curvature 17. Third fundamental form18. Characterization of the sphere as a locus of umbilical points; 19. Asymptotic lines; 20. Torsion of asymptotic lines; 21. Introduction of special parameter curves; 22. Asymptotic lines and lines of curvature as parameter curves; 23. Embedding a given arc in a system of parameter curves; 24. Analogues of polar coordinates on a surface; Chapter V Some Special Surfaces; 1. Surfaces of revolution; 2. Developable surfaces in the small made up of parabolic points; 3. Edge of regression of a developable; 4. Why the name developable? 5. Developable surfaces in the large1 |
| Record Nr. | UNINA-9910139601203321 |
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Stoker J. J (James Johnston), <1905->
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| New York, : Wiley-Interscience, 1989, c1969 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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