Riemannian Manifolds An Introduction to Curvature |
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| Author:
| Lee, John M. |
| Series title: | Graduate Texts in Mathematics Ser. |
| ISBN: | 978-0-387-98322-6 |
| Publication Date: | Sep 1997 |
| Publisher: | Springer
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| Book Format: | Paperback |
| List Price: | USD $54.95 |
Book Description:
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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.
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.