The characterizations on a class of weakly weighted Einstein-Finsler metrics

TL;DR

This paper investigates a specific class of Finsler metrics called weakly weighted Einstein-Finsler metrics, providing conditions for their isotropic curvature and complete characterizations using navigation expressions.

Contribution

It offers a complete characterization of weakly weighted Einstein-Kropina metrics through their navigation expressions and curvature conditions, advancing understanding in Finsler geometry.

Findings

Weakly weighted Einstein-Kropina metrics have isotropic S-curvature under certain conditions.

Complete characterization of these metrics via navigation expressions.

Conditions on weight constants influence the metrics' properties.

Abstract

In this paper, we study the weakly weighted Einstein-Finsler metrics. First, we show that weakly weighted Einstein-Kropina metrics must be of isotropic S-curvature with respect to the Busemann-Hausdorff volume form under a certain condition about the weight constants. Then we characterize weakly weighted Einstein-Kropina metrics completely via their navigation expressions or via $\alpha$ and $\beta$ respectively.