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.
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Research Article |
Authors | |
Publication Date | April 15, 2021 |
Acceptance Date | March 22, 2021 |
Published in Issue | Year 2021 Volume: 14 Issue: 1 |