Math 8260, Introduction to Riemannian Geometry

Spring 2007

Time and Place: T/R 12:30--01:45, 326 Boyd.
Instructor: Sa'ar Hersonsky
- E-mail: saarh@math.uga.edu
- Office: Boyd 447 Office Phone: 2587
- Office Hours: TBA

Course Description

This is an introductory course in Riemannian geometry. We will start with local properties of Riemannian manifolds and move into connections between local and global (topological and geometric) properties. Topics will include:

Riemannian metrics
Affine connections, Riemannian connections
Geodesics, convex neighborhoods
Curvature
Jacobi Fields
Isometric Immersions
Complete Manifolds, Hopf-Rinow and Hadamard Theorems.

If time permits we will discuss current directions of research. Mainly in Hyperbolic and negatively curved manifolds.

Prerequisites

A background of smooth manifolds and/or a basic course on curves and surfaces, as well as an understanding of the fundamental group (this will be needed in the last part of the course).

Grading

Grades will be based on weekly homework assignments. A detailed HW policy will be provided later.

Texts

I will be following closely

Do Carmo, Riemannian Geometry, Birkhauser, 1993.

However there are many other great books on the subject. Feel free to follow anyone you like.

Note:

I would highly recommend that you will all come to seminar talks and to the colloquium talks. In particular, this week consider attending Groves and Usher's colloq. talks, if you are interested in hearing a bit about state to the art research that is related to our course.
This coming week, since I am at a conference, will serve as a quick review (of things you should know...) and an introduction to Jason's research. Have fun!!!