●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
編輯手記

《微分幾何的各個方面》共分三卷，本卷是第三卷。本卷共包含三章內容，包括不變性理論、均勻性與局部均勻性及Ricci孤子。本卷主要討論了不變性理論，介紹了Weyl型和非Weyl型不變量，並從這個角度討論了Chern—Gauss—Bonnet公式，同時介紹了同質性、局部同質性、穩定性定理和Walker幾何，闡述了在黎曼、洛倫茲和仿射幾何的背景下出現的Ricci孤子。本書由淺入深，詳略得當，條理清晰，可以用作該學科的本科課程，也可作為研究生課程使用，同時適合高等院校師生及數學愛好者參考閱讀。