In this paper, we look at the projective relativity of (α, β)-metrics. Let α and α¯ be Riemannian metrics, and β and β¯ be non-zero one-forms on a manifold M of dimension at least 2. We give necessary and sufficient conditions for an (α, β)-metric F and an (α¯, β¯)-metric ¯ F to be projectively related. In particular this gives conditions for the polynomial (α, β)-metric and a generalized Kropina (α¯, β¯)-metric to be projectively related. We then investigate these conditions in more detail when F is assigned special curvature properties.

Keywords: Finsler metric, (&alpha,, &beta,)-metric, Projective change, Douglas metric and S-curvature