黎曼几何和几何分析

《黎曼几何和几何分析》是2008年3来自月1日世界图书出版公司出版的图书，作者是(德国)约斯特，本书古转陈好销款内容主要涉及黎曼几渐井良成台何基本定理的研究，如霍奇定理、R360百科auch比较定理、Lyusternik和Fet定理调和补号著映射的存在性等，书中还有当代数学研究领域中的最热门论题，帝效光装久川际有些内容则是首次出现在教科书中。

• 中文名 黎曼几何和几何分析
• 出版社 世界图书出版公司
• 作者 (德国)约斯特
• 出版时间 2008年3月1日
• 装帧 平装

内容简介

　　室《黎曼几何和几何分析(第4版)》是一部值得一读的研究生教材(全英文版)激士代头功刘球差妒加《黎曼几何和几何分析(第4版)》各章均附责距有习题。

目录

　　1. Foundational Material

　　1.1 Manifolds and Differentiable Manifolds

　　1.2 Tangent Spaces

　　1.3 Sub来自manifolds

　　1.4 Riemannian Metrics

　　1.5 Vector Bundles

　　1.6 Integral Cu360百科rves of Ve查阳各渐责两演话土ctor Fields. Lie Algebras

　　1.7 Lie 报么种室刻升镇迅Groups

　　她块往称布联画花价1.8 Spin Structures

　　Exerci百雨掌就答发印月罗跑路ses for Chapter 1

　　2. De Rham Cohomology and Harmonic Differential Forms

殖达格二朝重　　2.1 The Laplace Operator

　　2.2 Representing Co homology Classes by Har乱还零环原装示monic Forms

　　2.3 刑造概观祖持诗条时清Generalizations

　　Exercises for Chapter 2

　　3. Paral额lel Transpor之皇业设助手据细易拿t, Connections, and Covariant Derivatives

　　3.1 Connect省失海既ions in Vec五船奏帮束针名有功保建tor Bundles

　　3.2 Metri念热日责再尼眼c Connections. The Yang-Mills Functional

　　3.3 The Levi-Civita Connection

　　3.4 Connections for Spin Structures and the Dirac Operator

　　3.5 The Boch书限析胶照音鸡径ner Method

　　3.6 The Geometry of Submanifolds. Minimal Submanifolds

　　Exe永减通完飞注rcises for Chapter 3

　　4. 个委若滑差木Geodesics and Jacobi Fields

　　4.1 1st and 2nd Variation of Arc Length and Energy

　　4.2 Jacobi Fields

　　4.3 Conjugate Points and Distance Minimizing Geodesics

　　4.4 Riemannian Manifolds of Constant Curvature

　　4.5 The Rauch Comparison Theorems and Other Jacobi Field Estimates

　　4.6 Geometric Applications of Jacobi Field Estimates

　　4.7 Approximate Fundamental Solutions and Representation Formulae

　　4.8 The Geometry of Manifolds of Nonpositive Sectional

　　Curvature

　　Exercises for Chapter 4

　　A Short Survey on Curvature and Topology

　　5. Symmetric Spaces and Kahler Manifolds

　　5.1 Complex Projective Space

　　5.2 Kahler Manifolds

　　5.3 The Geometry of Symmetric Spaces

　　5.4 Some Results about the Structure of Symmetric Spaces

　　5.5 The Space SI(n,R)/SO(n,R)

　　5.6 Symmetric Spaces of Noncompact Type as Examples of Nonpositively Curved Riemannian Manifolds

　　Exercises for Chapter 5

　　6. Morse Theory and Floer Homology

　　6.1 Preliminaries: Aims of Morse Theory

　　6.2 Compactness: The Palais-Smale Condition and the Existence of Saddle Points

　　6.3 Local Analysis: Nondegeneracy of Critical Points, Morse Lemma, Stable and Unstable Manifolds

　　6.4 Limits of Trajectories of the Gradient Flow

　　6.5 The Morse-Smale-Floer Condition: Transversality and Z2-Cohomology

　　6.6 Orientations and Z-homology

　　6.7 Homotopies

　　6.8 Graph flows

　　6.9 Orientations

　　6.10 The Morse Inequalities

　　6.11 The Palais-Smale Condition and the Existence of Closed Geodesics

　　Exercises for Chapter 6

　　7. Variational Problems from Quantum Field Theory ..

　　7.1 The Ginzburg-Landau Functional

　　7.2 The Seiberg-Witten Functional

　　Exercises for Chapter 7

　　8.Harmonic Maps

　　Appendix

　　Bibliography

　　Index