Mth 626 Advanced Differential Geometry III

Topics selected from differentiable manifolds, differential forms, DeRham cohomology, Lie groups, fibre bundles, the Riemannian metric, affine and Riemannian connections, parallel translations, holonomy, geodesics, curvature, isometric embeddings and hypersurfaces, the Second Fundamental Form, complete Riemannian manifolds and the Hopf-Rinow theorem, spaces of constant curvature, variations of arc length, and the Morse Index theorem. This is the third course in a sequence of three: Mth 624, Mth 625, and Mth 626. Recommended prerequisite: Mth 425/525.