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.
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Series
39 primary booksGraduate Texts in Mathematics is a 39-book series with 39 primary works first released in 1899 with contributions by Peter J. Hilton, Urs Stammbach, and 37 others.