On a Class of Two-Dimensional Einstein Finsler Metrics of Vanishing S-Curvature

Abstract

An $(α,β)$-metric is defined by a Riemannian metric $α$ and $1$-form $β$. In this paper, we study a known class of two-dimensional $(α,β)$-metrics of vanishing S-curvature. We determine the local structure of those metrics and show that those metrics are Einsteinian (equivalently, isotropic flag curvature) but generally are not Ricci-flat.

11 pages