Invariant two-forms for geodesic flows (Q1891219)

Let \(M\) be an \(n\)-dimensional compact Riemannian manifold of negative sectional curvature with Anosov splitting of class \(C^ 1\). We investigate the space of continuous two-forms on the unit tangent bundle \(T^ 1 M\) of \(M\) which are invariant under the action of the geodesic flow. As an application we show that the metric and the topological entropy of the geodesic flow on \(T^ 1 M\) coincide if the Anosov splitting is of class \(C^ 2\).