Differential Geometry
Differentiable manifolds, tangent bundle, embedding theorems, vector fields and differential forms. Riemannian metrics and connections, geodesics, exponential map, and Jacobi fields. Generalizations of differential geometric concepts and applications.Differential forms. Integration on manifolds. Sard's Theorem. DeRham cohomology. Morse theory. Submanifolds and second fundamental form. Applications to geometric problems.
