Geodesic orbit spheres and constant curvature in Finsler geometry

TL;DR

This paper extends the classification of geodesic orbit spheres from Riemannian to Finsler geometry and shows that such spheres with constant flag curvature must be Randers, offering an alternative proof for certain homogeneous spheres.

Contribution

It generalizes the classification of geodesic orbit spheres to Finsler geometry and characterizes those with constant flag curvature as Randers metrics.

Findings

Geodesic orbit spheres in Finsler geometry are classified.

Such spheres with constant flag curvature are necessarily Randers.

Provides an alternative proof for invariant Finsler metrics with constant curvature on homogeneous spheres.

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 $K\equiv1$ on homogeneous spheres other than $Sp(n)/Sp(n-1)$.