MAT 568 
Differential
Geometry 

Fall 2015 
TTh 2:30-3:50
Physics P-128

Prof. Claude LeBrun.
Office: Math Tower 3-108.
Office hours: TTh 1:00-2:00


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.

Optional Textbook:

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 these in considerable detail. Knowing how to calculate is essential for a real understanding of this subject!


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☞Homework #2, Due 10/29/15☜
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Grades will be based on homework and class participation.

You may e-mail the professor by . This is the best method for making appointments outside normal office hours.

Stony Brook University expects students to maintain standards of personal integrity that are in harmony with the educational goals of the institution; to observe national, state, and local laws as well as University regulations; and to respect the rights, privileges, and property of other people. Faculty must notify the Office of Judicial Affairs of any disruptive behavior that interferes with their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.

DSS advisory. If you have a physical, psychiatric, medical, or learning disability that may affect your ability to carry out the assigned course work, please contact the office of Disabled Student Services (DSS), Humanities Building, room 133, telephone 632-6748/TDD. DSS will review your concerns and determine what accommodations may be necessary and appropriate. All information regarding any disability will be treated as strictly confidential.

Students who might require special evacuation procedures in the event of an emergency are urged to discuss their needs with both the instructor and DSS. For important related information, click here.

Illustration: Boy's surface arising from a minimal immersion of ℝℙ2 into S3.