Rigidity of negatively curved geodesic orbit Finsler spaces
  We prove some rigidity results on geodesic orbit Finsler spaces with non-positive curvature. In particular, we show that a geodesic Finsler space with strictly negative flag curvature must be a non-compact Riemannian symmetric space of rank one. 
Ming Xu and Shaoqiang Deng
math.DG