Riemannian Geometry
by Manfredo P. do Carmo · Manfredo P. do Carmo
Graduate textbook covering Riemannian metrics, affine and Levi-Civita connections, geodesics, curvature, Jacobi fields, the Hopf-Rinow and Hadamard theorems, and comparison theorems. Readers who know basic smooth manifolds learn to compute with curvature and prove classical global results.
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