Free Delivery Over $100
|
|
|||
|
||||
OverviewThis text is designed for a one-quarter or one-semester graduate couse in 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 the 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 ides 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 hasjust 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 mateiral not covered in the body of the text, but they also provide the students with indispensable practice in using the Full Product DetailsAuthor: John M. LeePublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 1997 ed. Volume: 176 Dimensions: Width: 15.50cm , Height: 1.30cm , Length: 23.50cm Weight: 0.790kg ISBN: 9780387983226ISBN 10: 0387983228 Pages: 226 Publication Date: 05 September 1997 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Replaced By: 9783319917542 Format: Paperback Publisher's Status: Out of Print Availability: Out of print, replaced by POD  We will order this item for you from a manufatured on demand supplier. 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. <br>Nieuw Archief voor Wiskunde, September 2000 This 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 |
||||
