The generalized unicorn problem on -metrics

In this paper, we study the generalized unicorn problem on regular ( α , β ) -metrics in the form of F = α ϕ ( 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.