THE UNIT BUNDLE OF A REAL HYPERBOLIC SPACE

The purpose of this article is to study the two homogeneous structures of the unit bundle of a real hyperbolic space, namely and In both the cases, we determine the -invariant Riemannian metrics. In passing, we examine whether the geodesic flow is an isometry of when equipped with its Levi-Civita metric. Finally, we study the manifold of geodesics of seen as a homogeneous space.