On Homogeneous Landsberg Surfaces

Akbar Tayebi; Behzad Najafi

doi:10.1016/j.geomphys.2021.104314

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arXiv · 2104.01680

On Homogeneous Landsberg Surfaces

Akbar Tayebi·Behzad Najafi

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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.

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BibTeX RIS

Akbar Tayebi, Behzad Najafi. 2021-04-04. On Homogeneous Landsberg Surfaces. https://doi.org/10.1016/j.geomphys.2021.104314

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