On Einstein Matsumoto metrics

Abstract

This paper contributes to the study of Matsumoto metrics F = α2/α-β with β of constant length related to α, where the α is a Riemannian metric and the β is a one form. It is shown that such a Matsumoto metric F is an Einstein metric if and only if α is Ricci-flat and β is parallel with respect to α. A nontrivial example of Ricci flat Matsumoto metrics is given.