Basic concepts of (pseudo) Riemannian geometry, such as curvature and Ricci tensors, Riemannian distance, geodesics, the Laplacian, and proofs of some fundamental results, including the Frobenius and Lie-subgroup theorems, the local structure of constant-curvature metrics, characterization of conformal flatness, the Hopf-Rinow, Myers, Lichnerowicz and Singer-Thorpe theorems.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.