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,...
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| 主要作者: | |
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| 企業作者: | |
| 格式: | 電子 電子書 |
| 語言: | English |
| 出版: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2008.
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| 版: | 1st ed. 2008. |
| 叢編: | Lecture Notes in Mathematics,
1764 |
| 主題: | |
| 在線閱讀: | https://doi.org/10.1007/978-3-540-45330-7 |
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書本目錄:
- 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.