A class of Einstein ( α, β)-metrics.

In this paper, we study a special class of Finsler metrics, called ( α, β)-metrics, which are defined by F = αϕ( β/α), where α is a Riemannian metric and β is a 1-form. We show that if ϕ = ϕ( s) is a polynomial in s, it is Einstein if and only if it is Ricci-flat. We also determine the Ricci-flat ( α, β)-metrics which are not of the type F = ( α + ɛβ)/ α. [ABSTRACT FROM AUTHOR]