On the degree of geodesic mobility of Riemannian manifolds

Abstract

We will consider the definition of the degree r of geodesic mobility of a Riemannian manifold and will prove that the well-known results on the geodesic mobility are essentially local. In the last section of our paper, we will prove that the geodesic mobility of an n-dimensional closed, simply-connected Riemannian manifold with positive constant sectional curvature satisfies the identity r D .n C 1/.n C 2/=2, n 2.