黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载 2025

黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载 2025

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黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载 2025

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　　《黎曼几何》非常值得一读。

内容简介

　　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。

内页插图

目录

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

黎曼几何 [Riemannian Geometry] epub pdf mobi txt 电子书 下载 2025

黎曼几何 [Riemannian Geometry] 下载 epub mobi pdf txt 电子书 2025

评分☆☆☆☆☆

一本不错的书，是正版

评分☆☆☆☆☆

很好的几何教材，值得一读！

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　　读这本书时，偶然还想到了我们日常对狂狷的理解大都错了。《论语·子路》中云：“不得中行而与之，必也狂狷乎。狂者进取，狷者有所不为也。”狂狷一词可以分开解，“狂”是对自己来说，“狷”是面对这个世界来说——自我进取，追求超越，是为狂；沉默以对，不敏俗事，是为狷。反观那些文青艺青，其狂不过作态，其狷更不必说。惟有一个人道德无亏，才有资格评价那些道德有亏的。——“你们中间谁是没有罪的，谁就可以先拿石头打她。”（《约翰福音》）

评分☆☆☆☆☆

需要认真在实习的知识。感谢。

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3 An Introduction to Gröbner Bases, William W. Adams, Philippe Loustaunau (1994, ISBN 978-0-8218-3804-4)

评分☆☆☆☆☆

　　希望自己不是一个太狼狈的"坏蛋"；

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很经典的一部教材，打算好好研究一下，包装也还可以，京东物流比较快，比当当快多了

评分☆☆☆☆☆

　　如果置身釜底，

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