Lectures on Symplectic Geometry

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures,...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Cannas da Silva, Ana (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2008.
Edición:1st ed. 2008.
Colección:Lecture Notes in Mathematics, 1764
Temas:
Geometry, Differential.
Differential equations.
Differential Geometry.
Differential Equations.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Symplectic Manifolds
  • Symplectic Forms
  • Symplectic Form on the Cotangent Bundle
  • Symplectomorphisms
  • Lagrangian Submanifolds
  • Generating Functions
  • Recurrence
  • Local Forms
  • Preparation for the Local Theory
  • Moser Theorems
  • Darboux-Moser-Weinstein Theory
  • Weinstein Tubular Neighborhood Theorem
  • Contact Manifolds
  • Contact Forms
  • Contact Dynamics
  • Compatible Almost Complex Structures
  • Almost Complex Structures
  • Compatible Triples
  • Dolbeault Theory
  • Kähler Manifolds
  • Complex Manifolds
  • Kähler Forms
  • Compact Kähler Manifolds
  • Hamiltonian Mechanics
  • Hamiltonian Vector Fields
  • Variational Principles
  • Legendre Transform
  • Moment Maps
  • Actions
  • Hamiltonian Actions
  • Symplectic Reduction
  • The Marsden-Weinstein-Meyer Theorem
  • Reduction
  • Moment Maps Revisited
  • Moment Map in Gauge Theory
  • Existence and Uniqueness of Moment Maps
  • Convexity
  • Symplectic Toric Manifolds
  • Classification of Symplectic Toric Manifolds
  • Delzant Construction
  • Duistermaat-Heckman Theorems.

Ejemplares similares