Topics in Riemannian Geometry

Math 755 Syllabus

1. Review of differentiable manifold

2. Riemannian metrics

3. Connections and curvature

4. Geodesics and Jacobi fields

5. Spaces of Constant curvature

6. Classification Results

Hopf-Rinow, Morse index and Sphere theorems

Text: Riemannian Geometry by M. DoCarmo, Birkhauser

ISBN 3-7643-3490-8

Weekly exercises will be assigned and discussed.