Introduction to Riemannian manifolds / John M. Lee.

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Bibliographic Details
Main Author: Lee, John M., 1950- (Author)
Format: Book
Published: Cham : Springer, [2018]
Edition:Second edition.
Series:Graduate texts in mathematics ; 176.


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100 1 |a Lee, John M.,  |d 1950-  |e author. 
245 1 0 |a Introduction to Riemannian manifolds /  |c John M. Lee. 
246 3 |a Riemannian manifolds : an introduction to curvature 
250 |a Second edition. 
264 1 |a Cham :  |b Springer,  |c [2018] 
264 4 |c ©2018 
300 |a xiii, 437 pages :  |b illustrations ;  |c 25 cm. 
336 |a text  |b txt  |2 rdacontent 
337 |a unmediated  |b n  |2 rdamedia 
338 |a volume  |b nc  |2 rdacarrier 
490 1 |a Graduate texts in mathematics,  |x 0072-5285 ;  |v 176 
500 |a "Originally published with title 'Riemannian manifolds : an introduction to curvature'"--Title page verso. 
504 |a Includes bibliographical references (pages 415-418) and indexes. 
505 0 |a Preface -- 1. What Is Curvature? -- 2. Riemannian Metrics -- 3. Model Riemannian Manifolds -- 4. Connections -- 5. The Levi-Cevita Connection -- 6. Geodesics and Distance -- 7. Curvature -- 8. Riemannian Submanifolds -- 9. The Gauss-Bonnet Theorem -- 10. Jacobi Fields -- 11. Comparison Theory -- 12. Curvature and Topology -- Appendix A: Review of Smooth Manifolds -- Appendix B: Review of Tensors -- Appendix C: Review of Lie Groups -- References -- Notation Index -- Subject Index. 
520 |a This textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds. The second edition has been adapted, expanded, and aptly retitled from Lee's earlier book, Riemannian Manifolds: An Introduction to Curvature. Numerous exercises and problem sets provide the student with opportunities to practice and develop skills; appendices contain a brief review of essential background material. While demonstrating the uses of most of the main technical tools needed for a careful study of Riemannian manifolds, this text focuses on ensuring that the student develops an intimate acquaintance with the geometric meaning of curvature. The reasonably broad coverage begins with a treatment of indispensable tools for working with Riemannian metrics such as connections and geodesics. Several topics have been added, including an expanded treatment of pseudo-Riemannian metrics, a more detailed treatment of homogeneous spaces and invariant metrics, a completely revamped treatment of comparison theory based on Riccati equations, and a handful of new local-to-global theorems, to name just a few highlights. Reviews of the first edition: Arguments and proofs are written down precisely and clearly. The expertise of the author is reflected in many valuable comments and remarks on the recent developments of the subjects. Serious readers would have the challenges of solving the exercises and problems. The book is probably one of the most easily accessible introductions to Riemannian geometry. (M.C. Leung, MathReview) The book's aim is to develop tools and intuition for studying the central unifying theme in Riemannian geometry, which is the notion of curvature and its relation with topology. The main ideas of the subject, motivated as in the original papers, are introduced here in an intuitive and accessible way...The book is an excellent introduction designed for a one-semester graduate course, containing exercises and problems which encourage students to practice working with the new notions and develop skills for later use. By citing suitable references for detailed study, the reader is stimulated to inquire into further research. (C.-L. Bejan, zBMATH).--  |c Provided by publisher. 
650 0 |a Riemannian manifolds. 
830 0 |a Graduate texts in mathematics ;  |v 176. 
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