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編輯推薦

　　《黎曼幾何》非常值得一讀。

內容簡介

　　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。

內頁插圖

目錄

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

黎曼幾何 [Riemannian Geometry] 下載 mobi epub pdf txt 電子書

評分☆☆☆☆☆

好書，值得

評分☆☆☆☆☆

書沒問題，不知道為什麼同時拍的三本書，分瞭兩個包，有一本沒有塑封包裝

評分☆☆☆☆☆

　　希望自己不是一個太狼狽的"壞蛋"；

評分☆☆☆☆☆

ddj好謝謝你瞭解我嗎對啊對啊是啊所以我

評分☆☆☆☆☆

任一仿緊微分流形總具有黎曼度量，這種黎曼度量的數目是非常繁多的，但也不是完全任意的。微分流形的度量結構是受它的拓撲結構所製約的，而這種製約關係正是黎曼幾何研究的一個重要內容，還存在許多沒有解決的問題。

評分☆☆☆☆☆

還可以，還可以！

評分☆☆☆☆☆

幾何大師do Carmo先生的大作，復旦推薦書單中有很高評價

評分☆☆☆☆☆

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

評分☆☆☆☆☆

1827年，高斯發錶瞭《關於麯麵的一般研究》的著作，這在微分幾何的曆史上有重大的意義，它的理論奠定瞭現代形式麯麵論的基礎。微分幾何發展經曆瞭150年之後，高斯抓住瞭微分幾何中最重要的概念和帶根本性的內容，建立瞭麯麵的內在幾何學。其主要思想是強調瞭麯麵上隻依賴於第一基本形式的一些性質，例如麯麵上麯麵的長度、兩條麯綫的夾角、麯麵上的一區域的麵積、測地綫、測地綫麯率和總麯率等等。他的理論奠定瞭近代形式麯麵論的基礎。

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