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.
General
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