Finsler spaces whose geodesics are orbits

In this paper, we study Finsler spaces whose geodesics are the orbits of one-parameter subgroups of the group of isometries (abbreviated as Finsler g.o. spaces). We first generalize some geometric results on Riemannian g.o. spaces to the Finslerian setting. Then we show that a Finsler g.o. nilmanifold is at most two step nilpotent and construct some examples of g.o. spaces which are neither Berwaldian nor weakly symmetric. Further, we give a sufficient and necessary condition for a Randers space to be a g.o. space. Finally, we show that every Clifford–Wolf homogeneous Finsler space is a Finsler g.o. space.