The holonomy of spherically symmetric projective Finsler metrics of constant curvature

In this paper, we investigate the holonomy group of n-dimensional projective Finsler metrics of constant curvature. We establish that in the spherically symmetric case, the holonomy group is maximal, and for a simply connected manifold it is isomorphic to Diffₒ (S^{n-1}), the connected component of the identity of the group of smooth diffeomorphism on the (n-1) -dimensional sphere. In particular, the holonomy group of the n-dimensional standard Funk metric and the Bryant-Shen metrics are maximal and isomorphic to Diffₒ (S^{n-1}). These results are the firsts describing explicitly the holonomy group of n-dimensional Finsler manifolds in the non-Berwaldian (that is when the canonical connection is non-linear) case.