仿射和韦尔几何应用

本书主要介绍了仿射和外尔几何的应用。全书共分四章内容，主要研究了Walker结构、黎曼扩张等。第一章对基本的概念进行了全面的介绍；第二章和第三章研究了与流形上的仿射结构相关的各种黎曼扩张及其余切束上中性特征的相应度量，它们在涉及曲率算符的光谱几何和表面上的均匀连接的各种问题中发挥作用；第四章讨论了Kahler-Weyl流形，它在某种意义上介于仿射几何和Kahler-Weyl几何之间。本书由浅入深，详略得当，条理清晰，适合相关专业的高等院校师生参考阅读。

Preface
Acknowledgments
1 Basic Notions and Concepts
1.1 Basic Manifold Theory
1.2 Connections
1.3 Curvature Models in the Real Setting
1.4 Kaihler Geometry
1.5 Curvature Decompositions
1.6 Walker Structures
1.7 Metrics on the Cotangent Bundle
1.8 Self-dual Walker Metrics
1.9 Recurrent Curvature
1.10 Constant Curvature
1.11 The Spectral Geometry of the Curvature Tensor
2 The Geometry of Deformed Riemannian Extensions
2.1 Basic Notational Conventions
2.2 Examples ofAffine Osserman Ivanov-Petrova Manifolds
2.3 The Spectral Geometry of the Curvature Tensor of Affine Surfaces
2.4 Homogeneous 2-Dimensional Affine Surfaces
2.5 The Spectral Geometry of the Curvature Tensor of Deformed Riemannian
Extensions
3 The Geometry of Modified Riemannian Extensions
3.1 Four-dimensional Osserman Manifolds and Models
3.2 para-KShler Manifolds of Constant para-holomorphic Sectional Curvature .
3.3 Higher-dimensional Osserman Metrics
3.4 Osserman Metrics with Non-trivial Jordan Normal Form
3.5 (Semi) para-complex Osserman Manifolds
4 (para)-Kahler-Weyl Manifolds
4.1 Notational Conventions
4.2 (para)-Kaihler-Weyl Structures ifm ≥ 6
4.3 (para)-Kaihler-Weyl Structures ifm = 4
4.4 (para)-Kaihler-Weyl Lie Groups ifm = 4
4.5 (para)-Kaihler-Weyl Tensors if m = 4
4.6 Realizability of (para)-Kahler-Weyl Tensors if m = 4
Bibliography
Authors' Biographies
Index