In this article, we study a rich class of Finsler metrics which are defined by a Riemannian metric a and a 1-form b on a C¥ manifold. They are called (a;b )-metrics. We consider the non-Riemannian quantity H of a class of Einstein (a;b )-metrics that is called Ricci-flat (a;b )-metrics. We prove that every Ricci-flat Douglas (a;b )-metric has the vanishing H-curvature.
