Math 765 Riemannian Geometry (Spring 2011)

Lectures
Lectures are by Jeff Viaclovsky on Tuesdays and Thursdays at 2:30-3:45 PM in Van Vleck B231.
Textbooks
Foundations of Differentiable Manifolds and Lie Groups by Warner
Riemannian Geometry by Petersen
Differential Geometry Volumes I & II by Spivak.
Morse Theory by John Milnor.
Riemannian Manifolds: An Introduction to Curvature by John Lee.
Riemannian Geometry by Do Carmo.
Mailing List
The class mailing list is math765-1-s11 "at" lists.wisc.edu.
Examinations and Homework
There will be some suggested homework assignments and no exams.
- HW #1: TBA.
Brief lecture outline
- Hodge Theory in Chapter 6 of Warner, and more generally for elliptic operators between vector bundles.
- Riemannian connection and covariant differentiation of tensor fields.
- Bochner-Weitzenbock formulas on differential forms.
- Clifford algebras and manifolds with positive curvature operator.
- Algebra of curvature tensors.
- Asymptotic expansion of metric in normal coordinates.
- TBA.