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Overview"This text is designed for a one-quarter or one-semester graduate course on Riemannian geometry. It focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. The book begins with a careful treatment of the machinery of metrics, connections, and geodesics, and then introduces the Riemann curvature tensor, before moving on to submanifold theory, in order to give the curvature tensor a concrete quantitative interpretation. The remainder of the text is devoted to proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet's Theorem, and a special case of the Cartan-Ambrose- Hicks theorem. This unique volume will especially appeal to students by presenting a selective introduction to the main ideas of the subject in an easily accessible way. The material is ideal for a single course, but broad enough to provide students with a firm foundation from which to pursue research or develop applications in Riemannian geometry and other fields that use its tools. Of special interest are the ""exercises"" and ""problems"" dispersed throughout the text. The exercises are carefully chosen and timed so as to give the reader opportunities to review material that has just been introduced, to practice working with the definitions, and to develop skills that are used later in the book. The problems that conclude the chapters are generally more difficult. They not only introduce new material not covered in the body of the text." Full Product DetailsAuthor: John M. LeePublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 1997 ed. Volume: 176 Dimensions: Width: 15.60cm , Height: 1.50cm , Length: 23.40cm Weight: 1.160kg ISBN: 9780387982717ISBN 10: 038798271 Pages: 226 Publication Date: 05 September 1997 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Replaced By: 9783319917542 Format: Hardback Publisher's Status: Active Availability: Awaiting stock  The supplier is currently out of stock of this item. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out for you. Table of ContentsReviewsThis book is very well writen, pleasant to read, with many good illustrations. It deals with the core of the subject, nothing more and nothing less. Simply a recommendation for anyone who wants to teach or learn about the Riemannian geometry. Nieuw Archief voor Wiskunde, September 2000 Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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