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

简体网页||繁体网页

☆☆☆☆☆

[葡] 卡莫 著

出版社： 世界图书出版公司

ISBN：9787506292184

版次：1

商品编码：10096470

包装：平装

外文名称：Riemannian Geometry

开本：24开

出版时间：2008-05-01

用纸：胶版纸

页数：300

正文语种：英语

编辑推荐

　　《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

评分☆☆☆☆☆

一本不错的书，是正版

评分☆☆☆☆☆

很好

评分☆☆☆☆☆

是正品，看起来很不错。可以

评分☆☆☆☆☆

商品非常好，物流速度非常快，派送服務非常好，非常滿意，值得信賴

评分☆☆☆☆☆

很不错的数学书。

评分☆☆☆☆☆

还可以，还可以！

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☆☆☆☆☆

非常便宜非常好用！做活动很划算！满减叠加优惠券价格很实惠！！以后还会再买！！！！很好用！！！！

评分☆☆☆☆☆

微分几何 - 产生