Riemannian Geometry 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Chavel, Isaac 作者

Cambridge Univ Pr

译者

2006-4 出版日期

488 页数

$ 154.81 价格

HRD

丛书系列

9780521853682 图书编码

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发表于2024-09-19

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Riemannian Geometry 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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Riemannian Geometry 在线电子书图书描述

This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed by a selection of more specialized topics. Also featured are Notes and Exercises for each chapter, to develop and enrich the reader's appreciation of the subject. This second edition has a clearer treatment of many topics than the first edition, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. The main themes here are the effect of the curvature on the usual notions of classical Euclidean geometry, and the new notions and ideas motivated by curvature itself. Among the classical topics shown in a new setting is isoperimetric inequalities - the interplay of volume of sets and the areas of their boundaries - in curved spaces. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.

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