黎曼幾何 [Riemannian Geometry]

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

[葡] 卡莫 著
想要找書就要到 靜流書站
立刻按 ctrl+D收藏本頁
你會得到大驚喜!!
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

具體描述

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



用戶評價

評分

非常不錯!這次優惠買瞭好多本,包裝質量也很好,非常滿意!

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

快遞很快,書也是很好的,很喜歡。

評分

歡迎您撰寫這本書的原創書評

評分

  能錶白一下真我,

評分

評分

書質量好!

評分

書比較薄,當入門書瞭。

評分

書比較薄,當入門書瞭。

相關圖書

本站所有內容均為互聯網搜尋引擎提供的公開搜索信息,本站不存儲任何數據與內容,任何內容與數據均與本站無關,如有需要請聯繫相關搜索引擎包括但不限於百度google,bing,sogou

© 2025 windowsfront.com All Rights Reserved. 靜流書站 版權所有