On Homogeneous Randers Metrics

Year 2021, Volume: 14 Issue: 1, 217 - 225, 15.04.2021

Akbar Sadighi Megerdich Toomanian , Behzad Najafi

https://doi.org/10.36890/iejg.797112

Abstract

Keywords

Homogeneous metric

On Homogeneous Randers Metrics

Abstract

In this paper, we study the curvature features of the class of homogeneous Randers metrics. For these metrics, we first find a reduction criterion to be a Berwald metric based on a mild restriction on their Ricci tensors. Then, we prove that every homogeneous Randers metric with relatively isotropic (or weak) Landsberg curvature must be Riemannian. This provides an extension of well-known Deng-Hu theorem that proves the same result for a homogeneous Berwald-Randers metric of non-zero flag curvature.

Keywords

Homogeneous metric, Ricci tensor, Randers metric

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