Some Ricci-flat (?, ?)-metrics

Abstract

In this paper, we study a special class of Finsler metrics, (alpha, beta)-metrics, defined by F = alpha phi(beta/alpha), where alpha is a Riemannian metric and beta is a 1-form. We find an equation that characterizes Ricci -flat (a, fl) -metrics under the condition that the length of beta with respect to a is constant.