Instructor: David Glickenstein

Office: Mathematics 715

Office Phone: 621-2463

Office Hours: I will be available after class, or feel free to stop by my office or make an appointment

Email: glickenstein@math.arizona.edu

- Ricci Flow: An Introduction by Ben Chow and Dan Knopf
- T. Tao's blog on the Poincare Conjecture.
- Riemannian Geometry by Peter Petersen
- Foundations of Differentiable Manifolds and Lie Groups, by
Frank W. Warner

- Structure of 2D and 3D manifolds
- Ricci flow on surfaces. Last updated February 7, 2012
- Hodge Theory. Last updated March 2, 2012
- The Hopf fibration and 3D Lie groups. Last updated March 27, 2012.
- Convergence of Riemannian manifolds and applications. Last updated April 24, 2012.
- Discrete conformal
geometry (slides).

Instructor: David Glickenstein

Office: Mathematics 715

Office Phone: 621-2463

Office Hours: Monday 2-3 (in Math East 145), Tuesday 2-3 (in Math 715), Wednesday 10:30-11:30 (in Math 715)

Email: glickenstein@math.arizona.edu

- Riemannian Manifolds: An Introduction to Curvature by John Lee. He has errata here.

Other books of note:

- Elementary Differential Geometry Lecture Notes by Gilbert Weinstein.
- Riemannian Geometry by M. P. Do Carmo
- A Comprehensive Introduction to Differential Geometry by M. Spivak
- Riemannian Geometry: A Modern Introduction by I. Chavel
- Lectures on Differential Geometry by R. Schoen and S. T. Yau
- Comparison Theorems in Riemannian Geometry by J. Cheeger and D. Ebin
- Riemannian Geometry by Peter Petersen

- Notes from when I taught this class 2005-2006
- Notes from when I taught this class 2007-2008.
- Curves. Last updated August
22, 2011

- Introduction to symplectic geometry - Angel
- Existence of ODE - Shane
- Plateau's problem - Joe

- Existence of convex neighborhoods of points.
- First variation of area and minimal surfaces
- Formulation of geodesic equation as a Hamiltonian system
- Derivatives of the Riemannian distance function
- Thurston's 3D model geometries
- Hodge theorem
- Trigonometry on the sphere and hyperbolic space
- Areas of spherical triangles and hyperbolic triangles
- Geodesics on manifolds of revolution
- Examples of homogeneous spaces
- Isoperimetric inequality
- The existence of a triangulation on any surface
- Whitney's classification of surfaces