Basic Differential Geometry
Basic Differential Geometry (Spring Semester) – 60670
- Connections in vector bundles: Covariant derivative, parallel transport, orientability, curvature, baby Chern-Weil.
- Riemannian geometry: Levi Cevita connection, exponential map, Jacobi fields, arc length variation formulas, fundamental equations for metric immersions and submersions, space forms, Hopf-Rinow, Hadamard-Cartan, Bonnet- Myers (Gauss-Bonnet, Bochner technique).
- Other geometric structures: (one or more of Kahler manifolds, symplectic manifolds, contact manifolds).
References
- Chavel, Riemannian Geometry: A modern introduction.
- Grove, Riemannian geometry: A metric entrance.
- Petersen, Riemannian Geometry.
- Gallot, Hulin, and Lafontaine, Riemannian geometry.
- Cullen, Introduction to General Topology.
- Dugundji, Topology.
- Kelley, General Topology. Munkres, Topology.
- Steen, Counterexamples in Topology.