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

黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载 2022

黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载 2022


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发表于2022-05-16

商品介绍



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

黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载 2022



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书籍描述

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



黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载 2022

黎曼几何 [Riemannian Geometry] 下载 epub mobi pdf txt 电子书 2022

黎曼几何 [Riemannian Geometry] pdf 下载 mobi 下载 pub 下载 txt 电子书 下载 2022

黎曼几何 [Riemannian Geometry] mobi pdf epub txt 电子书 下载 2022

黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载
想要找书就要到 静思书屋
立刻按 ctrl+D收藏本页
你会得到大惊喜!!

读者评价

评分

京东的速度真是快,冲这点就好评

评分

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

评分

对想深入研究基础数学的人,这书值得一读。

评分

很经典的一部教材,打算好好研究一下,包装也还可以,京东物流比较快,比当当快多了

评分

do carmo 黎曼几何..

评分

孩子买的,我是看不懂

评分

goodgood

评分

测N95雷区呢就我发淋雨slow退恶徒咯五KKK

评分

这是一本国外经典的数学专业书籍,详细介绍了黎曼几何相关的知识,适合数学专业的研究生,或者本科生查阅。

黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载 2022

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黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载 2022









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