Lyapunov exponents and stiffness for geodesic flow

Sergio A. Romaña Ibarra

Universidade Federal do Rio de Janeiro (Brasil)

Abstract:

In this lecture we will show how conditions on Lyapunov exponents impose rigidity on geometry. More specifically, we will prove that if the geodesic flow of a surface is Anosov and the Lypunov exponents are constant in the set of closed geodesics, then the curvature is constant. This is a joint work with Nestor Nina Zarate.