MAT 568 

Fall 2007 
TTh 2:20-3:40
Physics P-122

Prof. Claude LeBrun.
Office: Math Tower 3-108.
Office hours: TTh 10:10-11:10

This course constitutes the first half of a two-semester introduction to Riemannian geometry. Presupposing only a basic familiarity with manifolds and tensor fields, we will first develop a working knowledge of Riemannian metrics, connections, and curvature. We will then begin our study of the interplay between topology and curvature.

Prerequisite: Geometry/Topology II, a passing grade on the comprehensive exam, or the professor's expressed permission.

Text: Riemannian Geometry, by Manfredo Do Carmo, Birkhäuser, 1992.

Homework exercises will be assigned frequently, but only collected on a sporadic basis. You will be expected to work all of these in complete detail. Failure to do so may result in a complete inability to understand much of the material.

Grades will be based on homework and class participation.

The Professor may be reached by e-mail at . This is the best method for making appointments outside normal office hours.

DSS advisory. If you have a physical, psychiatric, medical, or learning disability that could adversely affect your ability to carry out assigned course work, please contact the Disabled Student Services office (DSS), Educational Communications Center (ECC) Building, room 128, (631) 632-6748.  DSS will review your situation and determine, with you, what accommodations are necessary and appropriate. All information and documentation regarding disabilities will be treated as strictly confidential.

Students for whom special evacuation procedures might be necessary in the event of an emergency are encouraged to discuss their needs with both the instructor and with DSS. Important information regarding these issues can also be found at the following web site: