GENERALIZED UNICORNS PROBLEM WITH A SPECIAL ($\alpha, \beta$)-METRIC

In this paper, we study the generalized unicorns problem on regular (α, β)-metrics in the form of F = αφ(s), s = 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 special polynomial in s, then F is a weak Landsberg metric if and only if F is a Berwald metric. Further, we prove that if φ = φ(s) is a polynomial in s and F is not a Randers metric, then F is of relatively isotropic mean Landsberg curvature if and only if it is a Berwald metric.