Autore	Lang Serge
Edizione	[3rd ed. 1995.]
Pubbl/distr/stampa	New York, NY : , : Springer New York : , : Imprint : Springer, , 1995
Descrizione fisica	1 online resource (XIV, 364 p.)
Disciplina	516.36
Altri autori (Persone)	LangSerge <1927-2005.>
Collana	Graduate Texts in Mathematics
Soggetto topico	Differential geometry Mathematical analysis Analysis (Mathematics) Algebraic topology Differential Geometry Analysis Algebraic Topology
ISBN	1-4612-4182-0
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	I Differential Calculus -- §1. Categories -- §2. Topological Vector Spaces -- §3. Derivatives and Composition of Maps -- §4. Integration and Taylor’s Formula -- §5. The Inverse Mapping Theorem -- II Manifolds -- §1. Atlases, Charts, Morphisms -- §2. Submanifolds, Immersions, Submersions -- §3. Partitions of Unity -- §4. Manifolds with Boundary -- III Vector Bundles -- §1. Definition, Pull Backs -- §2. The Tangent Bundle -- §3. Exact Sequences of Bundles -- §4. Operations on Vector Bundles -- §5. Splitting of Vector Bundles -- IV Vector Fields and Differential Equations -- §1. Existence Theorem for Differential Equations -- §2. Vector Fields, Curves, and Flows -- §3. Sprays -- §4. The Flow of a Spray and the Exponential Map -- §5. Existence of Tubular Neighborhoods -- §6. Uniqueness of Tubular Neighborhoods -- V Operations on Vector Fields and Differential Forms -- §1. Vector Fields, Differential Operators, Brackets -- §2. Lie Derivative -- $3. Exterior Derivative -- §4. The Poincaré Lemma -- §5. Contractions and Lie Derivative -- §6. Vector Fields and 1-Forms Under Self Duality -- §7. The Canonical 2-Form -- §8. Darboux’s Theorem -- VI The Theorem of Frobenius -- §1. Statement of the Theorem -- §2. Differential Equations Depending on a Parameter -- §3. Proof of the Theorem -- §4. The Global Formulation -- §5. Lie Groups and Subgroups -- VII Metrics -- §1. Definition and Functoriality -- §2. The Hilbert Group -- §3. Reduction to the Hilbert Group -- §4. Hilbertian Tubular Neighborhoods -- §5. The Morse—Palais Lemma -- §6. The Riemannian Distance -- §7. The Canonical Spray -- VIII Covariant Derivatives and Geodesics -- §1. Basic Properties -- §2. Sprays and Covariant Derivatives -- §3. Derivative Along a Curve and Parallelism -- §4. The Metric Derivative -- §5. More Local Results on the Exponential Map -- §6. Riemannian Geodesic Length and Completeness -- IX Curvature -- §1. The Riemann Tensor -- §2. Jacobi Lifts -- §3. Application of Jacobi Lifts to dexpx -- §4. The Index Form, Variations, and the Second Variation Formula -- §5. Taylor Expansions -- X Volume Forms -- §1. The Riemannian Volume Form -- §2. Covariant Derivatives -- §3. The Jacobian Determinant of the Exponential Map -- §4. The Hodge Star on Forms -- §5. Hodge Decomposition of Differential Forms -- XI Integration of Differential Forms -- §1. Sets of Measure 0 -- §2. Change of Variables Formula -- §3. Orientation -- §4. The Measure Associated with a Differential Form -- XII Stokes’ Theorem -- §1. Stokes’ Theorem for a Rectangular Simplex -- §2. Stokes’ Theorem on a Manifold -- §3. Stokes’ Theorem with Singularities -- XIII Applications of Stokes’ Theorem -- §1. The Maximal de Rham Cohomology -- §2. Moser’s Theorem -- §3. The Divergence Theorem -- §4. The Adjoint of d for Higher Degree Forms -- §5. Cauchy’s Theorem -- §6. The Residue Theorem -- Appendix The Spectral Theorem -- §1. Hilbert Space -- §2. Functionals and Operators -- §3. Hermitian Operators.
Record Nr.	UNINA-9910789224303321

Autore	Bär Christian
Edizione	[1st ed. 2014.]
Pubbl/distr/stampa	Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014
Descrizione fisica	1 online resource (VIII, 187 p.)
Disciplina	516.36
Collana	Lecture Notes in Mathematics
Soggetto topico	Differential geometry Algebraic topology Differential Geometry Algebraic Topology
ISBN	3-319-07034-7
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Differential Characters and Geometric Chains -- Relative differential Cohomology -- Index.
Record Nr.	UNINA-9910300147903321

Autore	Do Carmo Manfredo P
Edizione	[1st ed. 1994.]
Pubbl/distr/stampa	Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1994
Descrizione fisica	1 online resource (X, 118 p.)
Disciplina	515/.37
Collana	Universitext
Soggetto topico	Differential geometry Mathematical analysis Analysis (Mathematics) Mathematical physics Physics Differential Geometry Analysis Theoretical, Mathematical and Computational Physics Mathematical Methods in Physics Numerical and Computational Physics, Simulation
ISBN	3-642-57951-5
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	1. Differential Forms in Rn -- 2. Line Integrals -- 3. Differentiable Manifolds -- 4. Integration on Manifolds; Stokes Theorem and Poincaré’s Lemma -- 1. Integration of Differential Forms -- 2. Stokes Theorem -- 3. Poincaré’s Lemma -- 5. Differential Geometry of Surfaces -- 1. The Structure Equations of Rn -- 2. Surfaces in R3 -- 3. Intrinsic Geometry of Surfaces -- 6. The Theorem of Gauss-Bonnet and the Theorem of Morse -- 1. The Theorem of Gauss-Bonnet -- 2. The Theorem of Morse -- References.
Record Nr.	UNINA-9910480715803321

Edizione	[1st ed. 1981.]
Pubbl/distr/stampa	Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1981
Descrizione fisica	1 online resource (VII, 329 p. 2 illus.)
Disciplina	530.15
Collana	Lecture Notes in Physics
Soggetto topico	Physics Mathematical physics Differential geometry Mathematical Methods in Physics Mathematical Physics Differential Geometry
ISBN	3-540-38573-8
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	On a geometric quantization scheme generalizing those of Kostant-Souriau and Czyz -- Further applications of geometric quantization -- General vector field representations of local Heisenberg systems -- Aspects of relativistic quantum mechanics on phase space -- On the confinement of magnetic poles -- SU(3) and SU(4) as spectrum-generating groups -- The phase space for the Yang-Mills equations -- Instantons in nonlinear ?-models, gauge theories and general relativity -- Gauge-theoretical foundation of color geometrodynamics -- Non-associative algebras and exceptional gauge groups -- Atiyah-Singer index theorem and quantum field theory -- Topological concepts in phase transition theory -- Life without T2 -- Affine model of internal degrees of freedom in a non-euclidean space -- Jet bundles and weyl geometry -- Line fields and Lorentz manifolds -- The manifold of embeddings of a closed manifold -- The manifold of embeddings of a non-compact manifold.
Record Nr.	UNINA-9910257447403321

Edizione	[1st ed. 1991.]
Pubbl/distr/stampa	Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1991
Descrizione fisica	1 online resource (XIX, 404 p. 4 illus.)
Disciplina	516.3/6
Collana	Lecture Notes in Physics
Soggetto topico	Mathematical physics Differential geometry Theoretical, Mathematical and Computational Physics Differential Geometry
ISBN	3-540-47090-5
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Higgs fields and superconnections -- Noncommutative differential geometry, quantum mechanics and gauge theory -- to non-commutative geometry and Yang-Mills model-building -- II. Gauge-field model-building via non-commutative differential geometry -- Measuring coalgebras, quantum group-like objects, and non-commutative geometry -- Tensor Operator Structures in Quantum Unitary Groups -- Quantum groups and quantum complete integrability: Theory and experiment -- Some ideas and results on integrable nonlinear evolution systems -- An algebraic characterization of complete integrability for Hamiltonian systems -- Integrable lattice models and their scaling limits QFT and CFT -- Quantum groups, Riemann surfaces and conformal field theory -- Some physical applications of category theory -- From poisson groupoids to quantum groupoids and back -- Quantization on Kähler manifolds -- A new class of infinite-dimensional Lie algebras (continuum Lie algebras) and associated nonlinear systems -- Exchange Algebra in the Conformal Affine sl 2 Toda Field Theory -- Some properties of p-lines -- Breaking of supersymmetry through anomalies in composite spinor operators -- Conformal field theory and moduli spaces of vector bundles over variable Riemann surfaces -- Instanton homology -- W- geometry -- Connections between CFT and topology via Knot theory -- Stochastic calculus in superspace and supersymmetric Hamiltonians -- Geometric models and the modulli spaces for string theories -- Supersymmetric products of SUSY-curves ° -- Classical superspaces and related structures -- Remarks on the differential identities in Schouten-Nijenhuis algebra -- Generic irreducible representations of classical Lie superalgebras -- Krichever construction of solutions to the super KP hierarchies -- The structure of supersymplectic supermanifolds -- Gauge fixing: Geometric and probabilistic aspects of yang-mills gauge theories -- A renormalizable theory of quantum gravity -- Third order nonlinear Hamiltonian systems: Some remarks on the the action-angle transformation -- Tensor products of q p = 1 quantum groups and WZW fusion rules -- The modular group and super-KMS functionals -- New quantum representation for gravity and Yang-Mills theory -- Geometric quantization of the five-dimensional Kepler problem -- Structure functions on the usual and exotic symplectic and periplectic supermanifolds -- Symbols alias generating functionals — a supergeometric point of view -- Sheaves of graded Lie algebras over variable Riemann surfaces and a paired Weil-Petersson inner product.
Record Nr.	UNINA-9910257452703321