By John M. Lee
This textual content specializes in constructing an intimate acquaintance with the geometric which means of curvature and thereby introduces and demonstrates the entire major technical instruments wanted for a extra complicated direction on Riemannian manifolds. It covers proving the 4 such a lot basic theorems concerning curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a distinct case of the Cartan-Ambrose-Hicks Theorem.
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