a1 Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125, USA
We consider in this note smooth dynamical systems equipped with smooth invariant affine connections and show that, under a pinching condition on the Lyapunov exponents, certain invariant tensor fields are parallel. We then apply this result to a problem of rigidity of geodesic flows for Riemannian manifolds with negative curvature.
(Received May 10 1988)
† Partially supported by UNICAMP, Brazil.
‡ Partially supported by NSF Grant DMS 85-14630.