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.
| ISBN: | 9783030801069 |
| Publication date: | 5th August 2021 |
| Author: | John M Lee |
| Publisher: | Springer Nature Switzerland AG |
| Format: | Paperback |
| Pagination: | 437 pages |
| Series: | Graduate Texts in Mathematics |
| Genres: |
Differential and Riemannian geometry |