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书名：黎曼几何(第二版)
定价：148.0
ISBN：9787030182944
作者：Petersen, Peter
版次：1
出版时间：2016-06
内容提要：
暂时没有内容介绍，请见谅！
Preface Chapter 1.Riemannian Metrics Chapter 2.Curvature Chapter 3.Examples Chapter 4.Hypersurfaces Chapter 5.Geodesics and Distance Chapter 6.Sectional Curvature Comparison 1 Chapter 7.The Bochner Technique Chapter 8.Symmetric Spaces and Holonomy Chapter 9.Ricci Curvature Comparison Chapter 10.Convergence Chapter 11.Sectional Curvature Comparison 2 Appendix.De Rham Cohomology Bibliography Index
本书介绍黎曼几何中的重要技巧和定理，为满足那些希望专门研究黎曼几何的学生，书中还包含大量关于较深论题的背景材料。本书还介绍了*新的研究闷题。各种练习散布全书，帮助读者深入理解书中内容。本书是为数不多的整合了黎曼几何的几何和分析两方面内容的专*之一，适合熟悉张量和斯托克斯定理等流形理论的读者，可作为研究生一学年课程的教材。
目录：
Preface Chapter 1.Riemannian Metrics 1.Riemannian Manifolds and Maps 2.Groups and Riemannian Manifolds 3.Local Representations of Metrics 4.Doubly Warped Products 5.Exercises Chapter 2.Curvature 1.Connections 2.The Connection in Local Coordinates 3.Curvature 4.The Fundamental Curvature Equations 5.The Equations of Riemannian Geometry 6.Some Tensor Concepts 7.Further Study 8.Exercises Chapter 3.Examples 1.Computational Simplifications 2.Warped Products 3.Hyperbolic Space 4.Metrics on Lie Groups 5.Riemannian Submersions 6.Further Study 7.Exercises Chapter 4.Hypersurfaces 1.The Gauss Map 2.Existence of Hypersurfaces 3.The Gauss-Bonnet Theorem 4.Further Study 5.Exercises Chapter 5.Geodesics and Distance 1.Mixed Partials 2.Geodesics 3.The Metric Structure of a Riemannian Manifold 4.First Variation of Energy 5.The Exponential Map 6.Why Short Geodesics Are Segments 7.Local Geometry in Constant Curvature 8.Completeness 9.Characterization of Segments 10.Riemannian Isometries 11.Further Study 12.Exercises Chapter 6.Sectional Curvature Comparison I 1.The Connection Along Curves 2.Second Variation of Energy 3.Nonpositive Sectional Curvature 4.Positive Curvature 5.Basic Comparison Estimates 6.More on Positive Curvature 7.Further Study 8.Exercises Chapter 7.The Bochner Technique 1.Killing Fields 2.Hodge Theory 3.Harmonic Forms 4.Clifford Multiplication on Forms 5.The Curvature Tensor 6.Further Study 7.Exercises Chapter 8.Symmetric Spaces and Holonomy 1.Symmetric Spaces 2.Examples of Symmetric Spaces 3.Holonomy 4.Curvature and Holonomy 5.Further Study 6.Exercises Chapter 9.Ricci Curvature Comparison 1.Volume Comparison 2.Fundamental Groups and Ricci Curvature 3.Manifolds of Nonnegative Ricci Curvature 4.Further Study 5.Exercises Chapter 10.Convergence 1.Gromov-Hausdorff Convergence 2.Hōlder Spaces and Schauder Estimates 3.Norms and Convergence of Manifolds 4.Geometric Applications 5.Harmonic Norms and Ricci curvature 6.Further Study 7.Exercises Chapter 11.Sectional Curvature Comparison II 1.Critical Point Theory 2.Distance Comparison 3.Sphere Theorems 4.The Soul Theorem 5.Finiteness of Betti Numbers 6.Homotopy Finiteness 7.Further Study 8.Exercises Appendix.De Rham Cohomology 1.Lie Derivatives 2.Elementary Properties 3.Integration of Forms 4.C(ˇ)ech Cohomology 5.De Rham Cohomology 6.Poincaré Duality 7.Degree Theory 8.Further Study Bibliography Index
定价：148.0
ISBN：9787030182944
作者：Petersen, Peter
版次：1
出版时间：2016-06
内容提要：
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| 黎曼几何（第二版） | ||
 |
定价 | 148.00 |
| 出版社 | 科学出版社 | |
| 版次 | 1 | |
| 出版时间 | 2016年06月 | |
| 开本 | 16 | |
| 作者 | Petersen, Peter | |
| 装帧 | 圆脊精装 | |
| 页数 | 424 | |
| 字数 | 494 | |
| ISBN编码 | 9787030182944 | |
目录
Preface Chapter 1.Riemannian Metrics Chapter 2.Curvature Chapter 3.Examples Chapter 4.Hypersurfaces Chapter 5.Geodesics and Distance Chapter 6.Sectional Curvature Comparison 1 Chapter 7.The Bochner Technique Chapter 8.Symmetric Spaces and Holonomy Chapter 9.Ricci Curvature Comparison Chapter 10.Convergence Chapter 11.Sectional Curvature Comparison 2 Appendix.De Rham Cohomology Bibliography Index
关联推荐
本书介绍黎曼几何中的重要技巧和定理，为满足那些希望专门研究黎曼几何的学生，书中还包含大量关于较深论题的背景材料。本书还介绍了*新的研究闷题。各种练习散布全书，帮助读者深入理解书中内容。本书是为数不多的整合了黎曼几何的几何和分析两方面内容的专*之一，适合熟悉张量和斯托克斯定理等流形理论的读者，可作为研究生一学年课程的教材。
目录：
Preface Chapter 1.Riemannian Metrics 1.Riemannian Manifolds and Maps 2.Groups and Riemannian Manifolds 3.Local Representations of Metrics 4.Doubly Warped Products 5.Exercises Chapter 2.Curvature 1.Connections 2.The Connection in Local Coordinates 3.Curvature 4.The Fundamental Curvature Equations 5.The Equations of Riemannian Geometry 6.Some Tensor Concepts 7.Further Study 8.Exercises Chapter 3.Examples 1.Computational Simplifications 2.Warped Products 3.Hyperbolic Space 4.Metrics on Lie Groups 5.Riemannian Submersions 6.Further Study 7.Exercises Chapter 4.Hypersurfaces 1.The Gauss Map 2.Existence of Hypersurfaces 3.The Gauss-Bonnet Theorem 4.Further Study 5.Exercises Chapter 5.Geodesics and Distance 1.Mixed Partials 2.Geodesics 3.The Metric Structure of a Riemannian Manifold 4.First Variation of Energy 5.The Exponential Map 6.Why Short Geodesics Are Segments 7.Local Geometry in Constant Curvature 8.Completeness 9.Characterization of Segments 10.Riemannian Isometries 11.Further Study 12.Exercises Chapter 6.Sectional Curvature Comparison I 1.The Connection Along Curves 2.Second Variation of Energy 3.Nonpositive Sectional Curvature 4.Positive Curvature 5.Basic Comparison Estimates 6.More on Positive Curvature 7.Further Study 8.Exercises Chapter 7.The Bochner Technique 1.Killing Fields 2.Hodge Theory 3.Harmonic Forms 4.Clifford Multiplication on Forms 5.The Curvature Tensor 6.Further Study 7.Exercises Chapter 8.Symmetric Spaces and Holonomy 1.Symmetric Spaces 2.Examples of Symmetric Spaces 3.Holonomy 4.Curvature and Holonomy 5.Further Study 6.Exercises Chapter 9.Ricci Curvature Comparison 1.Volume Comparison 2.Fundamental Groups and Ricci Curvature 3.Manifolds of Nonnegative Ricci Curvature 4.Further Study 5.Exercises Chapter 10.Convergence 1.Gromov-Hausdorff Convergence 2.Hōlder Spaces and Schauder Estimates 3.Norms and Convergence of Manifolds 4.Geometric Applications 5.Harmonic Norms and Ricci curvature 6.Further Study 7.Exercises Chapter 11.Sectional Curvature Comparison II 1.Critical Point Theory 2.Distance Comparison 3.Sphere Theorems 4.The Soul Theorem 5.Finiteness of Betti Numbers 6.Homotopy Finiteness 7.Further Study 8.Exercises Appendix.De Rham Cohomology 1.Lie Derivatives 2.Elementary Properties 3.Integration of Forms 4.C(ˇ)ech Cohomology 5.De Rham Cohomology 6.Poincaré Duality 7.Degree Theory 8.Further Study Bibliography Index
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