MATH 765: Differential Geometry.
INSTRUCTOR: Ruifang Song.
office: 411 Van Vleck
e-mail: rsong AT math DOT wisc DOT edu
office hours: To be anounced.
CLASS SCHEDULE: (Jan 21, 2014-May 9, 2014)
MATH 765: 09:30-10:45 TR.
Course description
Syllabus
- Differentiable manifolds
- Lie groups and Lie algebras
- Riemannian metric, connection
- Geodesics, geodecics as solutions to a variation problem
- Curvature, tensor fields
- Jacobi fields, cojugate points
- Complete manifolds, Hopf-Rinow theorem, Hadamard theorem
- Spaces of constant sectional curvature
- Principle bundles, vector bundles and connections on them
- Riemannian holonomy groups
- Riemannian symmetric spaces
- Introduction to Kahler manifolds
- Introduction to Calabi-Yau manifolds
- ...
Tentative week-by-week schedule
HOMEWORK: Homework will be assigned about weekly.