On Homogeneous Landsberg Surfaces
Differential Geometry
2021-07-14 v1
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.
Cite
@article{arxiv.2104.01680,
title = {On Homogeneous Landsberg Surfaces},
author = {Akbar Tayebi and Behzad Najafi},
journal= {arXiv preprint arXiv:2104.01680},
year = {2021}
}