02469nam a22003378i 4500001001600000003000700016008004100023020001800064020001800082020001800100035002000118041000800138082001700146100002700163245007600190250002000266264007100286300003900357336002600396337002600422338003600448490005200484500001300536505032700549520103100876650002601907856005501933932003201988596000602020949010502026CR9780511616822UkCbUP090915s2006||||enk o ||1 0|eng|d a9780511616822 a9780521853682 a9780521619547 a(Sirsi) a796139 aeng00a516.3/732221 aChavel, Isaac,eauthor10aRiemannian geometry :ba modern introductionh[E-Book] /cIsaac Chavel. aSecond edition. 1aCambridge :bCambridge University Press,c2006e(CUP)fCUP20200108 a1 online resource (xvi, 471 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier aCambridge studies in advanced mathematics ;v98 aenglisch00gI.tRiemannian manifolds --gII.tRiemannian curvature --gIII.tRiemannian volume --gIV.tRiemannian coverings --gV.tSurfaces --gVI.tIsoperimetric inequalities (constant curvature) --gVII.tThe kinematic density --gVIII.tIsoperimetric inequalities (variable curvature) --gIX.tComparison and finiteness theorems. aThis 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. 0aGeometry, Riemannian.40uhttps://doi.org/10.1017/CBO9780511616822zVolltext aCambridgeCore (Order 30059) a1 aXX(796139.1)wAUTOc1i796139-1001lELECTRONICmZBrNsYtE-BOOKu8/1/2020xUNKNOWNzUNKNOWN1ONLINE