MATH 6620

Riemannian Geometry

Course Description

Course information provided by the 2026-2027 Catalog.

Topics include linear connections, Riemannian metrics and parallel translation; covariant differentiation and curvature tensors; the exponential map, the Gauss Lemma and completeness of the metric; isometries and space forms, Jacobi fields and the theorem of Cartan-Hadamard; the first and second variation formulas; the index form of Morse and the theorem of Bonnet-Myers; the Rauch, Hessian, and Laplacian comparison theorems; the Morse index theorem; the conjugate and cut loci; and submanifolds and the Second Fundamental form.

Prerequisites MATH 6520.

Last 4 Terms Offered 2025SP, 2023SP, 2021SP, 2019SP

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