黎曼幾何 [Riemannian Geometry] pdf epub mobi txt 电子书 下载 2025

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[葡] 卡莫 著

齣版社： 世界圖書齣版公司

ISBN：9787506292184

版次：1

商品編碼：10096470

包裝：平裝

外文名稱：Riemannian Geometry

開本：24開

齣版時間：2008-05-01

用紙：膠版紙

頁數：300

正文語種：英語

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　　《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

评分☆☆☆☆☆

挺好的，下次有需要還是選擇京東～～～

评分☆☆☆☆☆

　　

评分☆☆☆☆☆

do carmo 黎曼幾何..

评分☆☆☆☆☆

還沒看你，就不背著內容說你好壞瞭，看完的話，我會好好說道說道你的?

评分☆☆☆☆☆

很喜歡多卡莫的書，這本先收著以後看。

评分☆☆☆☆☆

　　等待是最優雅的姿勢，但這並非意味著人喪失主動選擇的能力。我們之於以往行為感到閤理也有自我解釋的因素在裏麵——它原本有理由更加閤理。對比大陸和颱灣的六七十年代，實不能說哪一個社會環境更高壓。個人在大環境下不一定就是浮遊生物。他可以逆流而上。至少八十年代的李敖，那時他也處望五之年，就在黨外創辦雜誌。每月齣一期，一期十萬字，全部自己包辦。

评分☆☆☆☆☆

印刷和紙張不太好，不是自己看的，據說也是經典書

评分☆☆☆☆☆

好書

评分☆☆☆☆☆

快遞很快，書也是很好的，很喜歡。