ON THE STRECH CURVATURE OF HOMOGENEOUS FINSLER METRICS
Abstract
In this paper, we prove that every homogeneous Finsler metric has relatively isotropic stretch curvature if and only if it is a Landsberg metric. It follows that every weakly Berwald homogeneous metric has relatively isotropic stretch curvature if and only if it is a Berwald metric. We show that a homogeneous metric of non-zero scalar flag curvature has relatively isotropic stretch curvature if and only if it is a Riemannian metric of constant sectional curvature. It turns out that a homogeneous (a,b)-metric with relatively isotropic stretch curvature is a Berwald metric. Also, it follows that a
homogeneous spherically symmetric metric with relatively isotropic stretch curvature reduces to a Riemannian metric. Finally, we prove that every homogeneous stretch-recurrent metric is a Landsberg metric.
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DOI: https://doi.org/10.22190/FUMI210804083K
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