On Homogeneous Landsberg Surfaces

Akbar Tayebi; Behzad Najafi

doi:10.1016/j.geomphys.2021.104314

paper

On Homogeneous Landsberg Surfaces

arXiv:2104.01680 · doi:10.1016/j.geomphys.2021.104314

Abstract

In this paper, we prove that every homogeneous Landsberg surface has isotropic flag curvature. Using this special form of the flag curvature, we prove a rigidity result on homogeneous Landsberg surface. Indeed, we prove that every homogeneous Landsberg surface is Riemannian or locally Minkowskian. This gives a positive answer to the Xu-Deng's well-known conjecture in 2-dimensional homogeneous Finsler manifolds.