ΓΕ3 - Riemannian Geometry
Syllabus
- Riemannian metrics, isometries, conformal maps.
- Geodesics and exponential maps.
- Parallel transport and holonomy.
- Hopf-Rinow’s Theorem.
- Curvature operator, Ricci curvature, scalar curvature.
- Riemannian submanifolds.
- Gauss-Codazzi-Ricci equations.
- 1st and 2nd variation of length.
- Jacobi fields.
- Comparison theorems.
- Homeomorphic sphere theorem