Comparison Theorems in Riemannian Geometry (AMS Chelsea Publishing) pdf epub mobi txt 電子書 下載 2024


Comparison Theorems in Riemannian Geometry (AMS Chelsea Publishing)

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Jeff Cheeger and David G. Ebin
American Mathematical Society
2008-08-04
165
USD 35.00
Hardcover
AMS Chelsea Publishing
9780821844175

圖書標籤: geometry  數學  微分幾何7  幾何分析  幾何  theorem  differential  comparison   


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发表于2024-12-23

Comparison Theorems in Riemannian Geometry (AMS Chelsea Publishing) epub 下載 mobi 下載 pdf 下載 txt 電子書 下載 2024

Comparison Theorems in Riemannian Geometry (AMS Chelsea Publishing) epub 下載 mobi 下載 pdf 下載 txt 電子書 下載 2024

Comparison Theorems in Riemannian Geometry (AMS Chelsea Publishing) pdf epub mobi txt 電子書 下載 2024



圖書描述

The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry.

The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem--the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius.

Chapters 6-9 deal with many of the most relevant contributions to the subject in the years 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is relaxed to a weak one, the failure can happen only in a restricted way, which can usually be classified up to isometry.

Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in 1975. Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field.

Some Reviews:

"... this is a wonderful book, full of fundamental techniques and ideas."

-- Robert L. Bryant, Director of the Mathematical Sciences Research Institute

"Cheeger and Ebin's book is a truly important classic monograph in Riemannian geometry, with great continuing relevance."

-- Rafe Mazzeo, Stanford University

"Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in 1975. Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field. To conclude, one can say that this book presents many interesting and recent results of global Riemannian geometry, and that by its well composed introductory chapters, the authors have managed to make it readable by non-specialists."

-- Zentralblatt MATH

Comparison Theorems in Riemannian Geometry (AMS Chelsea Publishing) 下載 mobi epub pdf txt 電子書

著者簡介

Cheeger is one of the major figures in modern differential geometry. He discovered together with his collegues some most famous theorems e.g. Splitting theorem, Soul theorem. And he is also a pioneer of metric geometry which is one of the major development of differential geometry at the end of 20th century.


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Comparison Theorems in Riemannian Geometry (AMS Chelsea Publishing) pdf epub mobi txt 電子書 下載
想要找書就要到 小哈圖書下載中心
立刻按 ctrl+D收藏本頁
你會得到大驚喜!!

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