《微分几何的各个方面》共分三卷，本卷是第三卷。本卷共包含三章内容，包括不变性理论、均匀性与局部均匀性及Ricci孤子。本卷主要讨论了不变性理论，介绍了Weyl型和非Weyl型不变量，并从这个角度讨论了Chern—Gauss—Bonnet公式，同时介绍了同质性、局部同质性、稳定性定理和Walker几何，阐述了在黎曼、洛伦兹和仿射几何的背景下出现的Ricci孤子。本书由浅入深，详略得当，条理清晰，可以用作该学科的本科课程，也可作为研究生课程使用，同时适合高等院校师生及数学爱好者参考阅读。
Preface
Acknowledgments
9 Invariance Theory
9.1 Review of Affine and Riemannian Geometry.
9.2 Invariance Theory in the Riemannian Setting
9.3 The Chern-Gauss-Bonnet Formula
9.4 Pseudo-Kaihler Manifolds
9.5 VSI Manifolds
9.6 Invariants that are not of Weyl Type
10 Homothety Homogeneity and Local Homogeneity
10.1 Introduction
10.2 Classification Results
10.3 Completeness
10.4 3-dimensional Walker Lorentzian Manifolds I: Curvature Homogeneity.
10.5 Walker Lorentzian Manifolds II: Homothety Curvature Homogeneity
10.6 Stability
10.7 Locally Homogeneous Metric G-structures
11 Ricci Solitons
11.1 Introduction
11.2 Riemanian Homogeneous Ricci Almost Solitons
11.3 Lorentzian Homogeneous Gradient Ricci Solitons
11.4 Riemannian Locally Conformally Flat Gradient Ricci Solitons
11.5 Lorentzian Locally Conformally Flat Gradient Ricci Solitons
11.6 Neutral Signature Self-dual Gradient Ricci Almost Solitons
Bibliography
Authors’Biographies
Index
编辑手记
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