Math 500: Differential Geometry
Official Course Description:
This class will introduce some of the fundamental objects in Riemannian geometry, giving the student ample opportunity to work with them in concrete examples. The following is a rough outline of topics to be covered:
- Differentiable manifolds, vector bundles, tensor bundles, and submanifolds
- Riemannian metrics and examples (including model spaces and Lie groups)
- Connections, affine connections, and the Riemannian connection
- Geodesics and the exponential map
- Curvature
- Jacobi fields
- The Hopf--Rinow theorem on complete Riemannian manifolds
- The Cartan--Hadamard theorem on the Riemannian cover of spaces with nonpositive curvature
- Spaces of constant sectional curvature
Texts:
- Manfredo do Carmo. (1992) Riemannian geometry.
- John M. Lee. (1997) Riemannian manifolds: an introduction to curvature.
Professor Kyle KINNEBERG
Office: HBH 452
Website: http://math.rice.edu/~kk43/
Lecture