Autore	Montgomery R (Richard), <1956->
Pubbl/distr/stampa	Providence, Rhode Island : , : American Mathematical Society, , 2009
Descrizione fisica	1 online resource (137 p.)
Disciplina	516.3/6
Collana	Memoirs of the American Mathematical Society
Soggetto topico	Jet bundles (Mathematics) Blowing up (Algebraic geometry) Pfaffian systems Singularities (Mathematics)
Soggetto genere / forma	Electronic books.
ISBN	1-4704-0570-9
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	""Contents""; ""Abstract""; ""Preface""; ""Chapter 1. Introduction""; ""1.1. The Monster construction""; ""1.2. Coordinates and the contact case""; ""1.3. Symmetries. Equivalence of points of the Monster""; ""1.4. Prolonging symmetries""; ""1.5. The basic theorem""; ""1.6. The Monster and Goursat distributions""; ""1.7. Our approach""; ""1.8. Proof of the basic theorem""; ""1.9. Plan of the paper""; ""Acknowledgements""; ""Chapter 2. Prolongations of integral curves. Regular, vertical, and critical curves and points ""; ""2.1. From Monster curves to Legendrian curves"" ""2.2. Prolonging curves""""2.3. Projections and prolongations of local symmetries""; ""2.4. Proof of Theorem 2.2""; ""2.5. From curves to points""; ""2.6. Non-singular points""; ""2.7. Critical curves""; ""2.8. Critical and regular directions and points""; ""2.9. Regular integral curves""; ""2.10. Regularization theorem""; ""2.11. An equivalent definition of a non-singular point""; ""2.12. Vertical and tangency directions and points""; ""Chapter 3. RVT classes. RVT codes of plane curves. RVT and Puiseux""; ""3.1. Definition of RVT classes"" ""3.2. Two more definitions of a non-singular point""""3.3. Types of RVT classes. Regular and entirely critical prolongations""; ""3.4. Classification problem: reduction to regular RVT classes""; ""3.5. RVT classes as subsets of PkR2 ""; ""3.6. Why tangency points?""; ""3.7. RVT code of plane curves""; ""3.8. RVT code and Puiseux characteristic""; ""Chapter 4. Monsterization and Legendrization. Reduction theorems""; ""4.1. Definitions and basic properties""; ""4.2. Explicit calculation of the legendrization of RVT classes""; ""4.3. From points to Legendrian curves"" ""4.4. Simplest classification results""""4.5. On the implications and shortfalls of Theorems 4.14 and 4.15""; ""4.6. From points to Legendrian curve jets. The jet-identification number ""; ""4.7. The parameterization number""; ""4.8. Evaluating the jet-identification number""; ""4.9. Proof of Proposition 4.44""; ""4.10. From Theorem B to Theorem 4.40""; ""4.11. Proof that critical points do not have a jet-identification number""; ""4.12. Proof of Proposition 4.26""; ""4.13. Conclusions. Things to come""; ""Chapter 5. Reduction algorithm. Examples of classification results"" ""5.1. Algorithm for calculating the Legendrization and the parameterization number""""5.2. Reduction algorithm for the equivalence problem""; ""5.3. Reduction algorithm for the classification problem""; ""5.4. Classes of small codimension consisting of a finite number of orbits""; ""5.5. Classification of tower-simple points""; ""5.6. Classes of high codimension consisting of one or two orbits""; ""5.7. Further examples of classification results; Moduli""; ""Chapter 6. Determination of simple points""; ""6.1. Tower-simple and stage-simple points""; ""6.2. Determination theorems"" ""6.3. Explicit description of stage-simple RVT classes""
Record Nr.	UNINA-9910481011703321

Autore	Laurent-Gengoux Camille
Edizione	[1st ed. 2013.]
Pubbl/distr/stampa	Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2013
Descrizione fisica	1 online resource (469 p.)
Disciplina	512.1 516.3/6
Collana	Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
Soggetto topico	Mathematical analysis Analysis (Mathematics) Differential geometry Topological groups Lie groups Nonassociative rings Rings (Algebra) Analysis Differential Geometry Topological Groups, Lie Groups Non-associative Rings and Algebras
ISBN	1-283-63084-2 9786613943293 3-642-31090-7
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Part I Theoretical Background:1.Poisson Structures: Basic Definitions -- 2.Poisson Structures: Basic Constructions -- 3.Multi-Derivations and Kähler Forms -- 4.Poisson (Co)Homology -- 5.Reduction -- Part II Examples:6.Constant Poisson Structures, Regular and Symplectic Manifolds -- 7.Linear Poisson Structures and Lie Algebras -- 8.Higher Degree Poisson Structures -- 9.Poisson Structures in Dimensions Two and Three -- 10.R-Brackets and r-Brackets -- 11.Poisson–Lie Groups -- Part III Applications:12.Liouville Integrable Systems -- 13.Deformation Quantization -- A Multilinear Algebra -- B Real and Complex Differential Geometry -- References -- Index -- List of Notations. .
Record Nr.	UNINA-9910438140103321

Autore	Goldman William Mark
Pubbl/distr/stampa	Providence, Rhode Island : , : American Mathematical Society, , [2008]
Descrizione fisica	1 online resource (86 p.)
Disciplina	516.3/6
Collana	Memoirs of the American Mathematical Society
Soggetto topico	Surfaces, Deformation of Riemann surfaces Geometry, Differential Geometry, Algebraic
Soggetto genere / forma	Electronic books.
ISBN	1-4704-0510-5
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	""Contents""; ""Introduction""; ""1. Equivalences of deformation theories""; ""2. The Betti and de Rham deformation theories and their moduli spaces""; ""2.1. The Betti groupoid""; ""2.2. The de Rham groupoid""; ""2.3. Equivalence of de Rham and Betti groupoids""; ""3. The Dolbeault groupoid""; ""3.1. Holomorphic line bundles""; ""3.2. The moduli spaces""; ""3.3. Geometric structure of the Dolbeault moduli space""; ""4. Equivalence of de Rham and Dolbeault groupoids""; ""4.1. Construction of the equivalence""; ""4.2. Higgs coordinates""; ""4.3. Involutions"" ""5. Hyperkahler geometry on the moduli space""""5.1. The quaternionic structure""; ""5.2. The Riemannian metric""; ""5.3. Complex-symplectic structure""; ""5.4. Quaternionization""; ""6. The twistor space""; ""6.1. The complex projective line""; ""6.2. The twistor space as a smooth vector bundle""; ""6.3. A holomorphic atlas for the twistor space""; ""6.4. The twistor lines""; ""6.5. The real structure on the twistor space""; ""6.6. Symplectic geometry of the twistor space""; ""6.7. The lattice quotient""; ""6.8. Functions and flows""; ""7. The moduli space and the Riemann period matrix"" ""7.1. Coordinates for the Betti moduli space""""7.2. Abelian differentials and their periods""; ""7.3. Flat connections""; ""7.4. Higgs fields""; ""7.5. The C-action in terms of the period matrix""; ""7.6. The C-action and the real points""; ""Bibliography""
Record Nr.	UNINA-9910480624203321

Autore	Falcitelli Maria <1954->
Pubbl/distr/stampa	Singapore ; ; River Edge, NJ, : World Scientific, 2004
Descrizione fisica	1 online resource (292 p.)
Disciplina	516.3/6
Altri autori (Persone)	PastoreAnna Maria <1945-> IanușStere
Soggetto topico	Riemannian submersions Geometry, Differential
Soggetto genere / forma	Electronic books.
ISBN	1-281-87229-6 9786611872298 981-256-233-8
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Riemannian Submersions and Related Topics; Preface; Contents; 1. Riemannian Submersions; 2. Submersions with Totally Geodesic Fibres; 3. Almost Hermitian Submersions; 4. Riemannian Submersions and Contact Metric Manifolds; 5. Einstein Spaces and Riemannian Submersions; 6. Riemannian Submersions and Submanifolds; 7. Semi-Riemannian Submersions; 8. Applications of Riemannian Submersions in Physics; Bibliography; Index
Record Nr.	UNINA-9910450136103321