点击选择搜索分类
首页 - 人力资源管理- 正文
☆☆☆☆☆
||
[德] 约斯特(Jost J.) 著
出版社: 世界图书出版公司 ISBN:9787510084447 版次:6 商品编码:11647751 包装:平装 外文名称:Riemannian Geometry and Geometric Analysis Sixth Edition 开本:24开 出版时间:2015-01-01 用纸:胶版纸 页数:611 正文语种:英文
It is the aim of this book to be a systematic and comprehensive introduction to Riemannian geometry and a representative introduction to the methods of geometric analysis. It attempts a synthesis of geometric and analytic methods in the study of Riemannian manifolds.
The present work is the sixth edition of my textbook on Riemannian geometry and geometric analysis. It has developed on the basis of several graduate courses I taught at the Ruhr~University Bochum and the University of Leipzig. The main new feature of the present edition is a systematic presentation of the spectrum of the Laplace operator and its relation with the geometry of the underlying Riemannian marufold. Naturally, I have also included several smaller additions and minor corrections (for which I am grateful to several readers). Moreover, the organization of the chapters has been systematically rearranged.
1.1 Manifolds and Differentiable Manifolds
1.2 Tangent Spaces
1.3 Submanifolds
1.4 Riemannian Metrics
1.5 Existence of Geodesics on Compact Manifolds
1.6 The Heat Flow and the Existence of Geodesics
1.7 Existence of Geodesics on Complete Manifolds
Exercises for Chapter 1
2 Lie Groups and Vector Bundles
2.1 Vector Bundles
2.2 Integral Curves of Vector Fields.Lie Algebras
2.3 Lie Groups
2.4 Spin Structures
Exercises for Chapter 2
3 The Laplace Operator and Harmonic Differential Forms
3.1 The Laplace Operator on Functions
3.2 The Spectrum of the Laplace Operator
3.3 The Laplace Operator on Forms
3.4 Representing Cohomology Classes by Harmonic Forms
3.5 Generalizations
3.6 The Heat Flow and Harmonic Forms
Exercises for Chapter 3
4 Connections and Curvature
4.1 Connections in Vector Bundles
4.2 Metric Connections.The Yang—Mills Functional
4.3 The Levi—Civita Connection
4.4 Connections for Spin Structures and the Dirac Operator
4.5 The Bochner Method
4.6 Eigenvalue Estimates by the Method of Li—Yau
4.7 The Geometry of Submanifolds
4.8 Minimal Submanifolds
Exercises for Chapter 4
5 Geodesics and Jacobi Fields
5.1 First and second Variation of Arc Length and Energy
5.2 Jacobi Fields
5.3 Conjugate Points and Distance Minimizing Geodesics
5.4 Riemannian Manifolds of Constant Curvature
5.5 The Rauch Comparison Theorems and Other Jacobi Field Estimates
5.6 Geometric Applications of Jacobi Field Estimates
5.7 Approximate Fundamental Solutions and Representation Formulas
5.8 The Geometry of Manifolds of Nonpositive Sectional Curvature
Exercises for Chapter 5
A Short Survey on Curvature and Topology
6 Symmetric Spaces and Kahler Manifolds
6.1 Complex Projective Space
6.2 Kahler Manifolds
6.3 The Geometry of Symmetric Spaces
6.4 Some Results about the Structure of Symmetric Spaces
6.5 The Space Sl(n,IR)/SO(n,IR)
6.6 Symmetric Spaces of Noncompact Type
Exercises for Chapter 6
7 Morse Theory and Floer Homology
7.1 Preliminaries: Aims of Morse Theory
7.2 The Palais—Smale Condition,Existence of Saddle Points
7.3 Local Analysis
7.4 Limits of Trajectories of the Gradient Flow
7.5 Floer Condition,Transversality and Z2—Cohomology
7.6 Orientations and Z—homology
7.7 Homotopies
7.8 Graph flows
7.9 Orientations
7.10 The Morse Inequalities
7.11 The Palais—Smale Condition and the Existence of Closed Geodesics
Exercises for Chapter 7
8 Harmonic Maps between Riemannian Manifolds
8.1 Definitions
8.2 Formulas for Harmonic Maps.The Bochner Technique
8.3 The Energy Integral and Weakly Harmonic Maps
8.4 Higher Regularity
8.5 Existence of Harmonic Maps for Nonpositive Curvature
8.6 Regularity of Harmonic Maps for Nonpositive Curvature
8.7 Harmonic Map Uniqueness and Applications
Exercises for Chapter 8
9 Harmonic Maps from Riemann Surfaces
9.1 Two—dimensional Harmonic Mappings
9.2 The Existence of Harmonic Maps in Two Dimensions
9.3 Regularity Results
Exercises for Chapter 9
10 Variational Problems from Quantum Field Theory
10.1 The Ginzburg—Landau Functional
10.2 The Seiberg—Witten Functional
10.3 Dirac—harmonic Maps
Exercises for Chapter 10
A Linear Elliptic Partial Differential Equations
A.1 Sobolev Spaces
A.2 Linear Elliptic Equations
A.3 Linear Parabolic Equations
B Fundamental Groups and Covering Spaces
Bibliography
Index
黎曼几何和几何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition] 电子书 下载 mobi epub pdf txt
黎曼几何和几何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition]-so88
黎曼几何和几何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
[德] 约斯特(Jost J.) 著
出版社: 世界图书出版公司 ISBN:9787510084447 版次:6 商品编码:11647751 包装:平装 外文名称:Riemannian Geometry and Geometric Analysis Sixth Edition 开本:24开 出版时间:2015-01-01 用纸:胶版纸 页数:611 正文语种:英文
内容简介
Riemannian geometry is characterized, and research is oriented towards and shaped by concepts (geodesics, connections, curvature, ...) and objectives, in particular to understand certain classes of (compact) Riemannian manifolds defined by curvature conditions (constant or positive or negative curvature, ...). By way of contrast, geometric analysis is a perhaps somewhat less systematic collection of techniques, for solving extremal problems naturally arising in geometry and for investigating and characterizing their solutions. It turns out that the two fields complement each other very well; geometric analysis offers tools for solving difficult problems in geometry, and Riemannian geometry stimulates progress in geometric analysis by setting ambitious goals.It is the aim of this book to be a systematic and comprehensive introduction to Riemannian geometry and a representative introduction to the methods of geometric analysis. It attempts a synthesis of geometric and analytic methods in the study of Riemannian manifolds.
The present work is the sixth edition of my textbook on Riemannian geometry and geometric analysis. It has developed on the basis of several graduate courses I taught at the Ruhr~University Bochum and the University of Leipzig. The main new feature of the present edition is a systematic presentation of the spectrum of the Laplace operator and its relation with the geometry of the underlying Riemannian marufold. Naturally, I have also included several smaller additions and minor corrections (for which I am grateful to several readers). Moreover, the organization of the chapters has been systematically rearranged.
内页插图
目录
1 Riemannian Manifolds1.1 Manifolds and Differentiable Manifolds
1.2 Tangent Spaces
1.3 Submanifolds
1.4 Riemannian Metrics
1.5 Existence of Geodesics on Compact Manifolds
1.6 The Heat Flow and the Existence of Geodesics
1.7 Existence of Geodesics on Complete Manifolds
Exercises for Chapter 1
2 Lie Groups and Vector Bundles
2.1 Vector Bundles
2.2 Integral Curves of Vector Fields.Lie Algebras
2.3 Lie Groups
2.4 Spin Structures
Exercises for Chapter 2
3 The Laplace Operator and Harmonic Differential Forms
3.1 The Laplace Operator on Functions
3.2 The Spectrum of the Laplace Operator
3.3 The Laplace Operator on Forms
3.4 Representing Cohomology Classes by Harmonic Forms
3.5 Generalizations
3.6 The Heat Flow and Harmonic Forms
Exercises for Chapter 3
4 Connections and Curvature
4.1 Connections in Vector Bundles
4.2 Metric Connections.The Yang—Mills Functional
4.3 The Levi—Civita Connection
4.4 Connections for Spin Structures and the Dirac Operator
4.5 The Bochner Method
4.6 Eigenvalue Estimates by the Method of Li—Yau
4.7 The Geometry of Submanifolds
4.8 Minimal Submanifolds
Exercises for Chapter 4
5 Geodesics and Jacobi Fields
5.1 First and second Variation of Arc Length and Energy
5.2 Jacobi Fields
5.3 Conjugate Points and Distance Minimizing Geodesics
5.4 Riemannian Manifolds of Constant Curvature
5.5 The Rauch Comparison Theorems and Other Jacobi Field Estimates
5.6 Geometric Applications of Jacobi Field Estimates
5.7 Approximate Fundamental Solutions and Representation Formulas
5.8 The Geometry of Manifolds of Nonpositive Sectional Curvature
Exercises for Chapter 5
A Short Survey on Curvature and Topology
6 Symmetric Spaces and Kahler Manifolds
6.1 Complex Projective Space
6.2 Kahler Manifolds
6.3 The Geometry of Symmetric Spaces
6.4 Some Results about the Structure of Symmetric Spaces
6.5 The Space Sl(n,IR)/SO(n,IR)
6.6 Symmetric Spaces of Noncompact Type
Exercises for Chapter 6
7 Morse Theory and Floer Homology
7.1 Preliminaries: Aims of Morse Theory
7.2 The Palais—Smale Condition,Existence of Saddle Points
7.3 Local Analysis
7.4 Limits of Trajectories of the Gradient Flow
7.5 Floer Condition,Transversality and Z2—Cohomology
7.6 Orientations and Z—homology
7.7 Homotopies
7.8 Graph flows
7.9 Orientations
7.10 The Morse Inequalities
7.11 The Palais—Smale Condition and the Existence of Closed Geodesics
Exercises for Chapter 7
8 Harmonic Maps between Riemannian Manifolds
8.1 Definitions
8.2 Formulas for Harmonic Maps.The Bochner Technique
8.3 The Energy Integral and Weakly Harmonic Maps
8.4 Higher Regularity
8.5 Existence of Harmonic Maps for Nonpositive Curvature
8.6 Regularity of Harmonic Maps for Nonpositive Curvature
8.7 Harmonic Map Uniqueness and Applications
Exercises for Chapter 8
9 Harmonic Maps from Riemann Surfaces
9.1 Two—dimensional Harmonic Mappings
9.2 The Existence of Harmonic Maps in Two Dimensions
9.3 Regularity Results
Exercises for Chapter 9
10 Variational Problems from Quantum Field Theory
10.1 The Ginzburg—Landau Functional
10.2 The Seiberg—Witten Functional
10.3 Dirac—harmonic Maps
Exercises for Chapter 10
A Linear Elliptic Partial Differential Equations
A.1 Sobolev Spaces
A.2 Linear Elliptic Equations
A.3 Linear Parabolic Equations
B Fundamental Groups and Covering Spaces
Bibliography
Index
前言/序言
黎曼几何和几何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition] 电子书 下载 mobi epub pdf txt
电子书下载地址:
相关电子书推荐:
- 文件名
- 速战速决的快乐收纳术
- 正版孕产妇饮食+运动+中医调养全书 值全彩珍藏版孕妇健康饮食指南 安全运动助产方法中医调养
- 书法入门-小牛顿百科馆
- 书 祝您好孕:不孕不育治疗指南
- 正版刚爱上科学——建筑与结构(双语版)9787115309990(英)Jackson
- 2000个怀孕胎教宜忌 王琪 江苏科学技术出版社
- 满58包邮 伴星共生 9787535795670 藤井旭 湖南科技出版社
- 去看恐龙化石咯-东方娃娃.贴纸游戏绘本
- 30秒探索:古罗马 马修·尼科尔斯
- 孩子爱吃的花式营养早餐
- 奥雅绘画小课堂-3-随书附赠奥雅密语卡
- 《好孕100道瘦孕料理》(孕期营养食谱) 怀孕书籍孕妇书籍孕妇食谱孕妇书籍 怀孕营养书孕妇
- 视觉天下探索发现丛书:解秘古今悬疑大案
- 李镇西教育书大全集全3册 爱心与教育+做*好的班主任+做*好的老师 素质教育探索手记
- 我们怎样接受不同-孩子们应该知道的秘密