黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载 2025

黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载 2025

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黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载 2025

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　　《黎曼几何》非常值得一读。

内容简介

　　The object of this book is to familiarize the reader with the basic language of and some fundamental theorems in Riemannian Geometry. To avoid referring to previous knowledge of differentiable manifolds， we include Chapter 0， which contains those concepts and results on differentiable manifolds which are used in an essential way in the rest of the book。
　　The first four chapters of the book present the basic concepts of Riemannian Geometry (Riemannian metrics， Riemannian connections， geodesics and curvature). A good part of the study of Riemannian Geometry consists of understanding the relationship between geodesics and curvature. Jacobi fields， an essential tool for this understanding， are introduced in Chapter 5. In Chapter 6 we introduce the second fundamental form associated with an isometric immersion， and prove a generalization of the Theorem Egregium of Gauss. This allows us to relate the notion of curvature in Riemannian manifolds to the classical concept of Gaussian curvature for surfaces。

内页插图

目录

Preface to the first edition
Preface to the second edition
Preface to the English edition
How to use this book
CHAPTER 0-DIFFERENTIABLE MANIFOLDS
1. Introduction
2. Differentiable manifolds；tangent space
3. Immersions and embeddings；examples
4. Other examples of manifolds，Orientation
5. Vector fields； brackets，Topology of manifolds

CHAPTER 1-RIEMANNIAN METRICS
1. Introduction
2. Riemannian Metrics

CHAPTER 2-AFFINE CONNECTIONS；RIEMANNIAN CONNECTIONS
1. Introduction
2. Affine connections
3. Riemannian connections

CHAPTER 3-GEODESICS；CONVEX NEIGHBORHOODS
1．Introduction
2．The geodesic flow
3．Minimizing properties ofgeodesics
4．Convex neighborhoods

CHAPTER 4-CURVATURE
1．Introduction
2．Curvature
3．Sectional curvature
4．Ricci curvature and 8calar curvature
5．Tensors 0n Riemannian manifoids

CHAPTER 5-JACOBI FIELDS
1．Introduction
2．The Jacobi equation
3．Conjugate points

CHAPTER 6-ISOMETRIC IMMERSl0NS
1．Introduction．
2．The second fundamental form
3．The fundarnental equations

CHAPTER 7-COMPLETE MANIFoLDS；HOPF-RINOW AND HADAMARD THEOREMS
1．Introduction．
2．Complete manifolds；Hopf-Rinow Theorem．
3．The Theorem of Hadamazd．

CHAPTER 8-SPACES 0F CONSTANT CURVATURE
1．Introduction
2．Theorem of Cartan on the determination ofthe metric by mebns of the　curvature．
3．Hyperbolic space
4．Space forms
5．Isometries ofthe hyperbolic space；Theorem ofLiouville

CHAPTER 9一VARIATl0NS 0F ENERGY
1．Introduction．
2．Formulas for the first and second variations of enezgy
3．The theorems of Bonnet—Myers and of Synge-WeipJtein

CHAPTER 10-THE RAUCH COMPARISON THEOREM
1．Introduction
2．Ttle Theorem of Rauch．
3．Applications of the Index Lemma to immersions
4．Focal points and an extension of Rauch’s Theorem

CHAPTER 11—THE MORSE lNDEX THEOREM
1．Introduction
2.The Index Theorem

CHAPTER 12-THE FUNDAMENTAL GROUP OF MANIFOLDS 0F NEGATIVE CURVATURE
1．Introduction
2．Existence of closed geodesics
CHAPTER 13-THE SPHERE THEOREM
References
Index

前言/序言

黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载 2025

黎曼几何 [Riemannian Geometry] 下载 epub mobi pdf txt 电子书 2025

评分☆☆☆☆☆

看过很有收获，好书推荐。

评分☆☆☆☆☆

书自然是经典，关键是印刷还不错。世图早先出的GTM系列有很多印得很差（不如字迹不清，歪页之类），但是这本黎曼几何，还有stein那套，这种彩色封面的，内页也印的很靓。应该收多一点。

评分☆☆☆☆☆

不错就是全英文的

评分☆☆☆☆☆

在这本书里我看见当年大批意气风发的文青、艺青散落在各地，青春和国家对他们而言都已成为一个空洞的字眼。再者，我读着他们写下的诗与文字，那股偏执而热浓郁的情感由于无处喷薄而变得更加炽烈，在地下奔走。这股炽烈最终指向了那个确定的靶子。

评分☆☆☆☆☆

配送快！！赞！！！

评分☆☆☆☆☆

微分几何学的产生和发展是和数学分析密切相连的。在这方面第一个做出贡献的是瑞士数学家欧拉。1736年他首先引进了平面曲线的内在坐标这一概念，即以曲线弧长这以几何量作为曲线上点的坐标，从而开始了曲线的内在几何的研究。

评分☆☆☆☆☆

4 The Integrals of Lebesgue, Denjoy, Perron, and Henstock, Russell A. Gordon (1994, ISBN 978-0-8218-3805-1)

评分☆☆☆☆☆

经典的几何书，好好好

评分☆☆☆☆☆

贵一点儿，不过值得仔细读。且是活动期间拿下的，心理平衡了。

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