On some projectively flat (alpha, beta)-metrics

Abstract

The (α β)-metric is a Finsler metric which is constructed from a Riemannian metric α and a differential 1-form β. We consider the projective flatness of Finsler spaces with some (α, β)-metrics. The purpose of the present paper is to find the conditions for a Finsler space with L = (α² ∕ (α - β)) + β and L = α + (βⁿ⁺¹ ∕ αⁿ).