Geodesic flows on manifolds of negative curvature with smooth horospheric foliations

摘要

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.We improve a result due to M. Kanai on the rigidity of geodesic flows on closed Riemannian manifolds of negative curvature whose stable or unstable (horospheric) foliation is smooth. More precisely, the main result proven here is: Let M be a closed [...] Riemannian manifold of negative sectional curvature. Assume the stable or unstable foliation of the geodesic flow [...] on the unit tangent bundle V of M is [...]. Assume moreover that either (a) the sectional curvature of M satisfies [...] or (b) the dimension of M is odd. Then the geodesic flow of M is [...]-isomorphic (i. e., conjugate under a [...] diffeomorphism between the unit tangent bundles) to the geodesic flow on a closed Riemannian manifold of constant negative curvature.