- 微分几何的各个方面(第2卷英文)/他山之石系列
- - 作者：(美)彼得·吉尔基//(韩)朴正阳//(西)拉蒙·瓦茨克斯-洛伦佐|责编:刘春雷//张嘉芮
  - 出版社：哈尔滨工业大学
  - ISBN：9787560391854
  - 出版日期：2020/12/01
  - 页数：221
- 售价：23.2

内容大纲
《微分几何的各个方面》共分三卷，本卷是第二卷，章节延续第一卷，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。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，适合高等院校师生及数学爱好者参考阅读。
作者介绍
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

内容大纲

作者介绍

目录

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