Geometry and Topology Seminar
Frame flow dynamics and rank rigidity
David Constantine, University of Michigan
Details
Wednesday April 18, 2007
809 Physical Sciences Center
4:00 pm / 3:30 tea
Abstract
Rank rigidity theorems seek to characterize locally symmetric spaces by geometric properties, namely geometric rank. The first theorem of this sort was the rank rigidity theorem of Ballmann and Burns-Spatzier. In this talk I'll present the following theorem: Suppose M is compact, has (Euclidean) rank 1 and along every geodesic in M there exists a parallel field making curvature -1 with the geodesic direction. Then if M is nonpositively curved for dim(M) odd, or has curvature pinched tightly enough for dim(M) even, M is hyperbolic. The proof relies on the dynamics of the frame flow.