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☆☆☆☆☆

书比较薄，当入门书了。

评分☆☆☆☆☆

评分☆☆☆☆☆

很不错的书呢，赞一个好评呢

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需要认真在实习的知识。感谢。

评分☆☆☆☆☆

2 Combinatorial Rigidity, Jack Graver, Brigitte Servatius, Herman Servatius (1993, ISBN 978-0-8218-3801-3)

评分☆☆☆☆☆

　　鲁迅在《杂感》中的那段议论：“无论爱什么，——饭，异性，国，民族，人类等等，——只有纠缠如毒蛇，执着如怨鬼，二六时中，没有已时者有望。”野夫先生这本书中我最喜欢的人物，是厨子黎爷。他知道自己能干什么，不能干什么。质而言之，他明白自己的真相，执着则建立在自知以上。在我们这个时代，如此已经难得。

评分☆☆☆☆☆

3 An Introduction to Gröbner Bases, William W. Adams, Philippe Loustaunau (1994, ISBN 978-0-8218-3804-4)

评分☆☆☆☆☆

5 Algebraic Curves and Riemann Surfaces, Rick Miranda (1995, ISBN

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　　当然，也还有另一个原因，野夫先生的嬉笑怒骂就是如此。他们是穿过黑暗年代的那一辈，忍受着屈辱与边缘化的放逐。每每想到野夫先生在大理的一处昏暗酒馆或者西藏青山下一夜一夜喝着酒，我就更能感到时代的罪恶。他们尚且还能潇洒，而不能离开家室的就更不必想。

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