On a class of Einstein-reversible Finsler metrics

In this paper, we introduce the notion of Einstein-reversibility for Finsler metrics. We study a class of p-power Finsler metrics defined by a Riemann metric and 1-form which are Einstein-reversible. It shows that such a class of Einstein-reversible Finsler metrics are always Einstein metrics. In particular, it indicates 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 determined for 2-dimensional square-root metrics which are Einsteinian, and such metrics are not necessarily Ricci-flat.