Differential Geometry

1 Course Unit

Riemannian metrics and connections, geodesics, completeness, Hopf- Rinow theorem, sectional curvature, Ricci curvature, scalar curvature, Jacobi fields, second fundamental form and Gauss equations, manifolds of constant curvature, first and second variation formulas, Bonnet- Myers theorem, comparison theorems, Morse index theorem, Hadamard theorem, Preissmann theorem, and further topics such as sphere theorems, critical points of distance functions, the soul theorem, Gromov- Hausdorff convergence. Not Offered Every Year Prerequisite: MATH 6000 AND MATH 6010 AND MATH 6020 AND MATH 6030 1 Course Unit