資料介紹

• 數學物理化學/理論科學

中文名: 黎曼幾何與幾何分析
原名: Riemannian Geometry and Geometric Analysis
別名: Universitext
作者: Jurgen Jost
資源格式: PDF
版本: 4th
出版社: Springer
書號: 3-540-42627-2
發行時間: 2000年
地區: 大陸,美國,英國,法國,德國
語言: 英文
黎曼幾何與幾何分析 簡介:

黎曼幾何與幾何分析 內容介紹：
《黎曼幾何與幾何分析》這是一本關於黎曼幾何，尤其是幾何分析的優秀教材，但是書中關於純黎曼幾何的講述很簡潔，不太適合初學者，書中很大篇幅在講幾何分析的基本方法，適合對黎曼幾何已經有一定了解想從分析方面深入研究的讀者。
《黎曼幾何和幾何分析》是一部值得一讀的研究生教材（全英文版），內容主要涉及黎曼幾何基本定理的研究，如霍奇定理、Rauch比較定理、Lyusternik和Fet定理調和映射的存在性等。《黎曼幾何和幾何分析》書中還有當代數學研究領域中的最熱門論題，有些內容則是首次出現在教科書中。
黎曼幾何與幾何分析 目錄:
1. Foundational Material
1.1 Manifolds and Differentiable Manifolds
1.2 Tangent Spaces
1.3 Submanifolds
1.4 Riemannian Metrics
1.5 Vector Bundles
1.6 Integral Curves of Vector Fields. Lie Algebras
1.7 Lie Groups
1.8 Spin Structures
Exercises for Chapter 1
2. De Rham Cohomology and Harmonic Differential Forms
2.1 The Laplace Operator
2.2 Representing Co homology Classes by Harmonic Forms
2.3 Generalizations
Exercises for Chapter 2
3. Parallel Transport, Connections, and Covariant Derivatives
3.1 Connections in Vector Bundles
3.2 Metric Connections. The Yang-Mills Functional
3.3 The Levi-Civita Connection
3.4 Connections for Spin Structures and the Dirac Operator ..
3.5 The Bochner Method
3.6 The Geometry of Submanifolds. Minimal Submanifolds ...
Exercises for Chapter 3
4. 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
黎曼幾何與幾何分 相關內容資料：
黎曼幾何引論
高等幾何與解析幾何
幾何畫板教程
微分幾何
微分幾何入門與廣義相對論
幾何畫板
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