Geodesic orbit spheres and constant curvature in Finsler geometry

Ming Xu

Geodesic orbit spheres and constant curvature in Finsler geometry

Differential Geometry 2018-05-08 v2

Authors: Ming Xu

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 $Sp(n)/Sp(n-1)$ .

Keywords

Finsler geometry geodesic orbit spheres constant flag curvature Randers metrics homogeneous spheres

Cite

@article{arxiv.1804.10780,
  title  = {Geodesic orbit spheres and constant curvature in Finsler geometry},
  author = {Ming Xu},
  journal= {arXiv preprint arXiv:1804.10780},
  year   = {2018}
}

Comments

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

Geodesic orbit spheres and constant curvature in Finsler geometry

Abstract

Keywords

Cite

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