000 02620nam a22003738i 4500
001 CR9780511616822
003 UkCbUP
005 20200124160219.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 090915s2006||||enk o ||1 0|eng|d
020 _a9780511616822 (ebook)
020 _z9780521853682 (hardback)
020 _z9780521619547 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA649
_b.C45 2006
082 0 0 _a516.3/73
_222
100 1 _aChavel, Isaac,
_eauthor.
245 1 0 _aRiemannian geometry :
_ba modern introduction /
_cIsaac Chavel.
250 _aSecond edition.
264 1 _aCambridge :
_bCambridge University Press,
_c2006.
300 _a1 online resource (xvi, 471 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge studies in advanced mathematics ;
_v98
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 _gI.
_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.
520 _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.
650 0 _aGeometry, Riemannian.
776 0 8 _iPrint version:
_z9780521853682
830 0 _aCambridge studies in advanced mathematics ;
_v98.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511616822
999 _c516557
_d516555