Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations

We are concerned with closed C ∞ riemannian manifolds of negative curvature whose geodesic flows have C ∞ stable and unstable foliations. In particular, we show that the geodesic flow of such a manifold is isomorphic to that of a certain closed riemannian manifold of constant negative curvature if the dimension of the manifold is greater than two and if the sectional curvature lies between − and −1 strictly.