Riemannian Geometry: A Modern Introduction

Riemannian Geometry: A Modern Introduction
ISBN-10
0521485789
ISBN-13
9780521485784
Series
Riemannian Geometry
Category
Mathematics
Pages
402
Language
English
Published
1995-01-27
Publisher
Cambridge University Press
Author
Isaac Chavel

Description

This book provides an introduction to Riemannian geometry, the geometry of curved spaces. Its main theme is the effect of the curvature of these spaces on the usual notions of geometry, angles, lengths, areas, and volumes, and those new notions and ideas motivated by curvature itself. Isoperimetric inequalities--the interplay of curvature with volume of sets and the areas of their boundaries--is reviewed along with other specialized classical topics. A number of completely new themes are created by curvature: they include local versus global geometric properties, that is, the interaction of microscopic behavior of the geometry with the macroscopic structure of the space. Also featured is an ambitious "Notes and Exercises" section for each chapter that will develop and enrich the reader's appetite and appreciation for the subject.

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