Riemannian Geometry

A Modern Introduction

Isaac Chavel - Collection Cambridge Studies in Advanced Mathematics

472 pages, parution le 15/03/2006 (2^eme édition)

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Résumé

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.

Assumes familiarity with differentiable manifolds so that more topics in Riemannian geometry can be treated
User-friendly presentation, with the right balance in notation and detail
The variety of advanced topics and the Notes and Exercises sections give great flexibility both in teaching from the book and for self-study

Sommaire

Riemannian manifolds
Riemannian curvature
Riemannian volume
Riemannian coverings
Surfaces
Isoperimetric inequalities (constant curvature)
The kinetic density
Isoperimetric inequalities (variable curvature)
Comparison and finiteness theorems

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Isaac Chavel
Collection	Cambridge Studies in Advanced Mathematics
Parution	15/03/2006
Édition	2^eme édition
Nb. de pages	472
Format	15 x 22,5
Couverture	Broché
Poids	645g
Intérieur	Noir et Blanc
EAN13	9780521619547
ISBN13	978-0-521-61954-7