作者：(美)彼得·吉尔基(Peter Gilk
页数：221页
出版社：哈尔滨工业大学出版社
出版日期：2020
ISBN：9787560391854
电子书格式：pdf/epub/txt
内容简介
《微分几何的各个方面》共分三卷，本卷是第二卷，章节延续第1卷，包含五章内容：第四章讨论了黎曼几何中的一些附加问题；第五章讨论了德雷姆上同调的基本性质，并简要介绍了特征类理论；第六章讨论了李群和李代数；在第七章中，给出了关于齐次空间和对称空间的指数映射，即经典群；在第八章中建立了单纯上同调、奇异上同调等之间的关系。 《微分几何的各个方面》由浅入深，详略得当，条理清晰，可以用作该学科的本科课程，适合高等院校师生及数学爱好者参考阅读。
目录
Preface
Acknowledgments
4 Additional Topics in Riemannian Geometry
4.1 Curves and Surfaces in Rn Given by ODEs
4.2 Volume of Geodesic Balls
4.3 Holomorphic Geometry
4.4 Kahler Geometry
5 de Rham Cohomology
5.1 Basic Properties of de Rham Cohomology
5.2 Clifford Algebras
5.3 The Hodge Decomposition Theorem
5.4 Characteristic Classes
6 Lie Groups
6.1 Basic Concepts
6.2 Lie Algebras
6.3 The Exponential Function of a Matrix Group
6.4 The Classical Groups
6.5 Representations of a Compact Lie Group
6.6 Bi-invariant pseudo-Riemannian Metrics
6.7 The Killing Form
6.8 The Classical Groups in Low Dimensions
6.9 The Cohomology of Compact Lie Groups
6.10 The Cohomology of the Unitary Group
7 Homogeneous Spaces and Symmetric Spaces
7.1 Smooth Structures on Coset Spaces
7.2 The Isometry Group
7.3 The Lie Derivative and Killing Vector Fields
7.4 Homogeneous Pseudo-Riemannian Manifolds
7.5 Local Symmetric Spaces
7.6 The Global Geometry of Symmetric Spaces
8 Other Cohomology Theories
8.1 Homological Algebra
8.2 Simplicial Cohomology
8.3 Singular Cohomology
8.4 Sheaf Cohomology
Bibliography
Authors’ Biographies
Index
编辑手记
Acknowledgments
4 Additional Topics in Riemannian Geometry
4.1 Curves and Surfaces in Rn Given by ODEs
4.2 Volume of Geodesic Balls
4.3 Holomorphic Geometry
4.4 Kahler Geometry
5 de Rham Cohomology
5.1 Basic Properties of de Rham Cohomology
5.2 Clifford Algebras
5.3 The Hodge Decomposition Theorem
5.4 Characteristic Classes
6 Lie Groups
6.1 Basic Concepts
6.2 Lie Algebras
6.3 The Exponential Function of a Matrix Group
6.4 The Classical Groups
6.5 Representations of a Compact Lie Group
6.6 Bi-invariant pseudo-Riemannian Metrics
6.7 The Killing Form
6.8 The Classical Groups in Low Dimensions
6.9 The Cohomology of Compact Lie Groups
6.10 The Cohomology of the Unitary Group
7 Homogeneous Spaces and Symmetric Spaces
7.1 Smooth Structures on Coset Spaces
7.2 The Isometry Group
7.3 The Lie Derivative and Killing Vector Fields
7.4 Homogeneous Pseudo-Riemannian Manifolds
7.5 Local Symmetric Spaces
7.6 The Global Geometry of Symmetric Spaces
8 Other Cohomology Theories
8.1 Homological Algebra
8.2 Simplicial Cohomology
8.3 Singular Cohomology
8.4 Sheaf Cohomology
Bibliography
Authors’ Biographies
Index
编辑手记
