This course is an introduction to Riemannian Geometry.

None yet.

There will be a midterm and a final. There will also be weekly homework.
Homework is posted to this website each Friday and due at the *start* of class the following Friday. Late homework will not be accepted.

- Homework 1, due April 12
- Homework 2, due April 19
- Homework 3, due April 26
- Homework 4, due May 3
- Homework 5, due May 10
- Homework 6, due May 17
- Homework 7, due May 24
- Homework 8, due May 31

The midterm was taken in class on Friday May 3rd.

The final was posted on Friday May 31st, and is due Friday June 7 at 1:30 (the answers should be handed in directly to Bena).

The skeleton of the syllabus is the following. Some topics will be covered very briefly. For more details see the notes and the subsection headings.

- Smooth manifolds
- Some examples
- Riemannian metrics
- Geodesics
- Curvature
- Lie groups and homogeneous spaces
- Characteristic classes
- Hodge theory
- Minimal surfaces

Notes from class will be posted online here and updated as we go along.

The following references are just suggestions. There are no required texts for the course.

- A. Besse Einstein manifolds
- J. Cheeger and D. Ebin Comparison theorems in Riemannian Geometry
- T. Colding and W. Minicozzi A course in minimal surfaces
- S. Kobayashi and K. Nomizu Foundations of Differential Geometry
- J. Milnor Morse Theory
- F. Warner Foundations of Differentiable Manifolds and Lie Groups