Geodesic orbit spheres and constant curvature in Finsler geometry

Abstract

In this paper, we generalize the classification of geodesic orbit spheres from Riemannian geometry to Finsler geometry. Then we further prove if a geodesic orbit Finsler sphere has constant flag curvature, it must be Randers. It provides an alternative proof for the classification of invariant Finsler metrics with $K\equiv 1$ on homogeneous spheres other than $Sp(n)/Sp(n-1)$.

In version 2 of this paper, a reference has been added, and a minor mistake in the introduction section has been corrected