An introduction to Lie groups and the geometry of homogeneous spaces /
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| Author / Creator: | Arvanitogeōrgos, Andreas, 1963- |
|---|---|
| Uniform title: | Homades Lie, homogeneis chōroi kai diaphorikē geōmetria. English |
| Imprint: | Providence, RI : American Mathematical Society, c2003. |
| Description: | xvi, 141 p. : ill. ; 22 cm. |
| Language: | English |
| Series: | Student mathematical library, 1520-9121 ; v. 22 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7786261 |
Table of Contents:
- Preface
- Introduction
- Chapter 1.. Lie Groups
- 1.. An example of a Lie group
- 2.. Smooth manifolds: A review
- 3.. Lie groups
- 4.. The tangent space of a Lie group - Lie algebras
- 5.. One-parameter subgroups
- 6.. The Campbell-Baker-Hausdorff formula
- 7.. Lie's theorems
- Chapter 2.. Maximal Tori and the Classification Theorem
- 1.. Representation theory: elementary concepts
- 2.. The adjoint representation
- 3.. The Killing form
- 4.. Maximal tori
- 5.. The classification of compact and connected Lie groups
- 6.. Complex semisimple Lie algebras
- Chapter 3.. The Geometry of a Compact Lie Group
- 1.. Riemannian manifolds: A review
- 2.. Left-invariant and bi-invariant metrics
- 3.. Geometrical aspects of a compact Lie group
- Chapter 4.. Homogeneous Spaces
- 1.. Coset manifolds
- 2.. Reductive homogeneous spaces
- 3.. The isotropy representation
- Chapter 5.. The Geometry of a Reductive Homogeneous Space
- 1.. G-invariant metrics
- 2.. The Riemannian connection
- 3.. Curvature
- Chapter 6.. Symmetric Spaces
- 1.. Introduction
- 2.. The structure of a symmetric space
- 3.. The geometry of a symmetric space
- 4.. Duality
- Chapter 7.. Generalized Flag Manifolds
- 1.. Introduction
- 2.. Generalized flag manifolds as adjoint orbits
- 3.. Lie theoretic description of a generalized flag manifold
- 4.. Painted Dynkin diagrams
- 5.. T-roots and the isotropy representation
- 6.. G-invariant Riemannian metrics
- 7.. G-invariant complex structures and Kahler metrics
- 8.. G-invariant Kahler-Einstein metrics
- 9.. Generalized flag manifolds as complex manifolds
- Chapter 8.. Advanced topics
- 1.. Einstein metrics on homogeneous spaces
- 2.. Homogeneous spaces in symplectic geometry
- 3.. Homogeneous geodesics in homogeneous spaces
- Bibliography
- Index
