The generalized unicorn problem on (α,β)-metrics

In this paper, we study the generalized unicorn problem on regular (α,β)-metrics in the form of F=αϕ(β/α), where α is a Riemannian metric and β is a 1-form on the manifold. We prove that, if ϕ=ϕ(s) is a polynomial in s, then F is a weak Landsberg metric if and only if F is a Berwald metric.