●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

本書主要介紹了仿射和外爾幾何的應用。全書共分四章內容，主要研究了Walker結構、黎曼擴張等。第一章對基本的概念進行了全面的介紹；第二章和第三章研究了與流形上的仿射結構相關的各種黎曼擴張及其餘切束上中性特征的相應度量，它們在涉及曲率算符的光譜幾何和表面上的均勻連接的各種問題中發揮作用；第四章討論了Kahler-Weyl流形，它在某種意義上介於仿射幾何和Kahler-Weyl幾何之間。本書由淺入深，詳略得當，條理清晰，適合相關專業的高等院校師生參考閱讀。