☆☆☆☆☆
簡體網頁||繁體網頁



下載連結1
下載連結2
下載連結3

類似圖書 點擊查看全場最低價

---

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☆☆☆☆☆

配送快！！贊！！！

評分☆☆☆☆☆

goodgood

評分☆☆☆☆☆

　　雖則李敖慣於吹捧，此戲劇性人格，亦這個時代讀書人的生存之道，不想苛求。但大多數既稱學者，又謂作傢，還兼任公共知識分子的。進一步說，我對這些還是感到懷疑。

評分☆☆☆☆☆

書自然是經典，關鍵是印刷還不錯。世圖早先齣的GTM係列有很多印得很差（不如字跡不清，歪頁之類），但是這本黎曼幾何，還有stein那套，這種彩色封麵的，內頁也印的很靚。應該收多一點。

評分☆☆☆☆☆

　　就多充一分勇士；

評分☆☆☆☆☆

在這本書裏我看見當年大批意氣風發的文青、藝青散落在各地，青春和國傢對他們而言都已成為一個空洞的字眼。再者，我讀著他們寫下的詩與文字，那股偏執而熱濃鬱的情感由於無處噴薄而變得更加熾烈，在地下奔走。這股熾烈最終指嚮瞭那個確定的靶子。

評分☆☆☆☆☆

Gooooooooooooooooooooood

評分☆☆☆☆☆

質量很好，品質保證。

評分☆☆☆☆☆

　　魯迅在《雜感》中的那段議論：“無論愛什麼，——飯，異性，國，民族，人類等等，——隻有糾纏如毒蛇，執著如怨鬼，二六時中，沒有已時者有望。”野夫先生這本書中我最喜歡的人物，是廚子黎爺。他知道自己能乾什麼，不能乾什麼。質而言之，他明白自己的真相，執著則建立在自知以上。在我們這個時代，如此已經難得。

類似圖書 點擊查看全場最低價