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

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 $\hat{I}\pm$ and ${\hat{I}}^2$ respectively.

22 pages