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　　《國外數學名著係列（影印版）30：黎曼幾何（第二版）》介紹黎曼幾何中的重要技巧和定理，為滿足那些希望專門研究黎曼幾何的學生，書中還包含大量關於較深論題的背景材料。《國外數學名著係列（影印版）30：黎曼幾何（第二版）》還介紹瞭新的研究問題。各種練習散布全書，幫助讀者深入理解書中內容。《國外數學名著係列（影印版）30：黎曼幾何（第二版）》是為數不多的整閤瞭黎曼幾何的幾何和分析兩方麵內容的專著之一，適閤熟悉張量和斯托剋斯定理等流形理論的讀者，可作為研究生一學年課程的教材。

內頁插圖

目錄

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．FurtherStudy
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—HausdorffConvergence
2．Holder 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．Cech Cohomology
5．De Rham Cohomology
6．Poincare Duality
7．Degree Theory
8．Further Study
Bibliography
Index

前言/序言

國外數學名著係列（影印版）30：黎曼幾何（第二版） 下載 mobi epub pdf txt 電子書

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