Introduction to Riemannian Manifolds (Graduate Texts in Mathematics, 176)
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Introduction to Riemannian Manifolds (Graduate Texts in Mathematics, 176)
<P>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.</P>
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