Introduction to Riemannian Manifolds

Author:   John M. Lee
Publisher:   Springer International Publishing AG
Edition:   2nd ed. 2018
Volume:   176
ISBN:  

9783319917542


Pages:   437
Publication Date:   14 January 2019
Format:   Hardback
Availability:   Manufactured on demand   Availability explained
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Introduction to Riemannian Manifolds


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Overview

This text 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. It covers 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.

Full Product Details

Author:   John M. Lee
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   2nd ed. 2018
Volume:   176
Weight:   0.836kg
ISBN:  

9783319917542


ISBN 10:   3319917544
Pages:   437
Publication Date:   14 January 2019
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

Table of Contents

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.

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Author Information

John Jack M. Lee is a professor of mathematics at the University of Washington. Professor Lee is the author of three highly acclaimed Springer graduate textbooks : Introduction to Smooth Manifolds, (GTM 218) Introduction to Topological Manifolds (GTM 202), and Riemannian Manifolds (GTM 176). Lee's research interests include differential geometry, the Yamabe problem, existence of Einstein metrics, the constraint equations in general relativity, geometry and analysis on CR manifolds.

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