Mathematics Colloquium

Thursday, October 12, 1995, 4:00pm

102 Bradley Hall

Professor Jeff Cheeger

New York University

speaks on

Spaces with Ricci curvature bounded from below

Abstract. The curvedness of a Riemannian manifold is measured by its curvature. In contrast to dimension two where there is only one notion of curvature, the classical Gaussian curvature, in higher dimensions, several notions are studied. Of current interest to both geometers and physicists are Ricci curvature, which occurs in the Einstein field equation. We will discuss the structure of manifolds whose Ricci curvature is bounded from below. The kind of results we will discuss can be illustrated from the Gauss-Bonnet theorem, from which it is easily seen that if the Gaussian curvature is positive, then the surface has to be the sphere. Therefore, conditions on curvature restrict the topology of manifolds. We will discuss higher dimensional analogue of this, and also study the metric structure of such manifolds.

Tea. High tea will be served at 3:30pm in the Lounge.
Emmy's. Certain refreshments will be available at the Emmy's after the talk.
Host. Shunhui Zhu will be the host, anybody interested in having dinner with the speaker should contact Shunhui (Ext. 6-3678).