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  • ISBN:9787560391854
  • 装帧:一般胶版纸
  • 册数:暂无
  • 重量:暂无
  • 开本:24cm
  • 页数:221页
  • 出版时间:2020-12-01
  • 条形码:9787560391854 ; 978-7-5603-9185-4

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
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