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OverviewFrom the preface:Many years have passed since the first edition. However, the encouragements of various readers and friends have persuaded us to write this third edition. During these years, Riemannian Geometry has undergone many dramatic developments. Here is not the place to relate them. The reader can consult for instance the recent book [Br5]. of our “mentor” Marcel Berger. However, Riemannian Geometry is not only a fascinating field in itself. It has proved to be a precious tool in other parts of mathematics. In this respect, we can quote the major breakthroughs in four-dimensional topology which occurred in the eighties and the nineties of the last century (see for instance [L2]). These have been followed, quite recently, by a possibly successful approach to the Poincaré conjecture. In another direction, Geometric Group Theory, a very active field nowadays (cf. [Gr6]), borrows many ideas from Riemannian or metric geometry. But let us stop hogging the limelight. This is justa textbook. We hope that our point of view of working intrinsically with manifolds as early as possible, and testing every new notion on a series of recurrent examples (see the introduction to the first edition for a detailed description), can be useful both to beginners and to mathematicians from other fields, wanting to acquire some feeling for the subject. Full Product DetailsAuthor: Sylvestre Gallot , Dominique Hulin , Jacques LafontainePublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 3rd ed. 2004 Dimensions: Width: 15.50cm , Height: 1.80cm , Length: 23.50cm Weight: 1.070kg ISBN: 9783540204930ISBN 10: 3540204938 Pages: 322 Publication Date: 30 July 2004 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsFrom the reviews of the third edition: This new edition maintains the clear written style of the original, including many illustrations ! examples and exercises (most with solutions). (Joseph E. Borzellino, Mathematical Reviews, 2005) This book based on graduate course on Riemannian geometry ! covers the topics of differential manifolds, Riemannian metrics, connections, geodesics and curvature, with special emphasis on the intrinsic features of the subject. Classical results ! are treated in detail. ! contains numerous exercises with full solutions and a series of detailed examples which are picked up repeatedly to illustrate each new definition or property introduced. For this third edition, some topics ! have been added and worked out in the same spirit. (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 50, (3-4), 2004) This book is based on a graduate course on Riemannian geometry and analysis on manifolds that was held in Paris. ! Classical results on the relations between curvature and topology are treated in detail. The book is almost self-contained, assuming in general only basic calculus. It contains nontrivial exercises with full solutions at the end. Properties are always illustrated by many detailed examples. (EMS Newsletter, December 2005) The guiding line of this by now classic introduction to Riemannian geometry is an in-depth study of each newly introduced concept on the basis of a number of reoccurring well-chosen examples ! . The book continues to be an excellent choice for an introduction to the central ideas of Riemannian geometry. (M. Kunzinger, Monatshefte fur Mathematik, Vol. 147 (1), 2006) From the reviews of the third edition: This new edition maintains the clear written style of the original, including many illustrations ... examples and exercises (most with solutions). (Joseph E. Borzellino, Mathematical Reviews, 2005) This book based on graduate course on Riemannian geometry ... covers the topics of differential manifolds, Riemannian metrics, connections, geodesics and curvature, with special emphasis on the intrinsic features of the subject. Classical results ... are treated in detail. ... contains numerous exercises with full solutions and a series of detailed examples which are picked up repeatedly to illustrate each new definition or property introduced. For this third edition, some topics ... have been added and worked out in the same spirit. (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 50, (3-4), 2004) This book is based on a graduate course on Riemannian geometry and analysis on manifolds that was held in Paris. ... Classical results on the relations between curvature and topology are treated in detail. The book is almost self-contained, assuming in general only basic calculus. It contains nontrivial exercises with full solutions at the end. Properties are always illustrated by many detailed examples. (EMS Newsletter, December 2005) The guiding line of this by now classic introduction to Riemannian geometry is an in-depth study of each newly introduced concept on the basis of a number of reoccurring well-chosen examples ... . The book continues to be an excellent choice for an introduction to the central ideas of Riemannian geometry. (M. Kunzinger, Monatshefte fur Mathematik, Vol. 147 (1), 2006) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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