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Riemannian geometry : = a modern introduction /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Riemannian geometry :/ Isaac Chavel.
Reminder of title:	a modern introduction /
Author:	Chavel, Isaac,
Description:	1 online resource (xvi, 471 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Geometry, Riemannian. -
Online resource:	https://doi.org/10.1017/CBO9780511616822
ISBN:	9780511616822 (ebook)

Riemannian geometry : = a modern introduction /
Chavel, Isaac,

Riemannian geometry :a modern introduction /Isaac Chavel. - Second edition. - 1 online resource (xvi, 471 pages) :digital, PDF file(s). - Cambridge studies in advanced mathematics ;98. - Cambridge studies in advanced mathematics ;134..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Riemannian manifolds --I.

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, first published in 2006, 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. 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.

ISBN: 9780511616822 (ebook)Subjects--Topical Terms:

672546
Geometry, Riemannian.

LC Class. No.: QA649 / .C45 2006

Dewey Class. No.: 516.3/73

Riemannian geometry : = a modern introduction /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 $g I. $t Riemannian manifolds -- $g II. $t Riemannian curvature -- $g III. $t Riemannian volume -- $g IV. $t Riemannian coverings -- $g V. $t Surfaces -- $g VI. $t Isoperimetric inequalities (constant curvature) -- $g VII. $t The kinematic density -- $g VIII. $t Isoperimetric inequalities (variable curvature) -- $g IX. $t Comparison and finiteness theorems.
520 $a 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, first published in 2006, 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. 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.
650 0 $a Geometry, Riemannian. $3 672546
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830 0 $a Cambridge studies in advanced mathematics ; $v 134. $3 1133579
856 4 0 $u https://doi.org/10.1017/CBO9780511616822