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Dynamics Seminar
October 31, 2007

Dave Constantine
University of Michigan

Ergodic Frame Flow and Hyperbolic Rank Rigidity

In this talk I'll present a rank rigidity result analogous to several previous results that identify locally symmetric spaces among general Riemannian manifolds via geometric rank. Specifically, I will show that, under some curvature restraints, a manifold which has along every geodesic a parallel vector field making curvature -1 with the geodesic direction is in fact of constant curvature -1. The proof proceeds by utilizing the ergodic theory of the frame flow.

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