黎曼幾何和幾何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition] epub pdf  mobi txt 電子書 下載

黎曼幾何和幾何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition] epub pdf mobi txt 電子書 下載 2024

黎曼幾何和幾何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition] epub pdf mobi txt 電子書 下載 2024


簡體網頁||繁體網頁
[德] 約斯特(Jost J.) 著

下載链接在页面底部


點擊這裡下載
    


想要找書就要到 靜思書屋
立刻按 ctrl+D收藏本頁
你會得到大驚喜!!

發表於2024-11-06

商品介绍



齣版社: 世界圖書齣版公司
ISBN:9787510084447
版次:6
商品編碼:11647751
包裝:平裝
外文名稱:Riemannian Geometry and Geometric Analysis Sixth Edition
開本:24開
齣版時間:2015-01-01
用紙:膠版紙
頁數:611
正文語種:英文

黎曼幾何和幾何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition] epub pdf mobi txt 電子書 下載 2024



类似图書 點擊查看全場最低價

相关書籍





書籍描述

內容簡介

  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.

內頁插圖

目錄

1 Riemannian Manifolds
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

前言/序言



黎曼幾何和幾何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition] epub pdf mobi txt 電子書 下載 2024

黎曼幾何和幾何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition] 下載 epub mobi pdf txt 電子書

黎曼幾何和幾何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition] pdf 下載 mobi 下載 pub 下載 txt 電子書 下載 2024

黎曼幾何和幾何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition] mobi pdf epub txt 電子書 下載 2024

黎曼幾何和幾何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition] epub pdf mobi txt 電子書 下載
想要找書就要到 靜思書屋
立刻按 ctrl+D收藏本頁
你會得到大驚喜!!

讀者評價

評分

必須給劉 強東點贊,很不錯,很便宜的,多搞點優惠活動是要錶揚的

評分

很不錯的一本書

評分

經典正版圖書,配送及時,非常滿意

評分

丘老的文集太難啃瞭,這本書作為入門恰到好處。

評分

不錯

評分

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 a

評分

很好

評分

必須給劉 強東點贊,很不錯,很便宜的,多搞點優惠活動是要錶揚的

評分

比如我們10歲以前,阿拉丁神燈這一類兒童書籍能夠打動我們,也能夠讓我們開始學著認識這個世界。然而當我們長大一些之後,能夠打動我們或者對我們有巨大幫助的書籍,會變化。所以第一個建議是:根據自己當前的人生階段、認知水平來思考自己應該看哪一類書,比如說初入職場的人,去學習具體的工作技能(如Excel的使用)會比研讀管理學理論要更為有益,因為對於這個階段的你來說,技能性的東西可以現學現練,很快就能把書裏的東西轉化為自己能力的一部分。

黎曼幾何和幾何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition] epub pdf mobi txt 電子書 下載 2024

类似图書 點擊查看全場最低價

黎曼幾何和幾何分析(第6版) [Riemannian Geometry and Geometric Analysis Sixth Edition] epub pdf mobi txt 電子書 下載 2024


分享鏈接





相关書籍


本站所有內容均為互聯網搜索引擎提供的公開搜索信息,本站不存儲任何數據與內容,任何內容與數據均與本站無關,如有需要請聯繫相關搜索引擎包括但不限於百度google,bing,sogou

友情鏈接

© 2024 book.tinynews.org All Rights Reserved. 靜思書屋 版权所有