On A Class of Finsler Metrics of Einstein-Reversibility

Abstract

In this paper, we introduce the notion of Einstein-reversibility for Finsler met- rics. We study a class of p-power Finsler metrics determined by a Riemann metric and 1-form which are of Einstein-reversibility. It shows that such a class of Finsler metrics of Einstein-reversibility are always Einstein metrics. In particular, we show that all p-power metrics but Randers metrics, square metrics and 2-dimensional square-root metrics, are always Ricci-flat-parallel. Further, the local structure is almost determined for 2-dimensional square-root metrics which are Einsteinian (equivalently, of isotropic flag curvature), and examples show such metrics are not necessarily Ricci-flat.