Some Ricci-flat ( α ,β )-metrics

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