  Finsleroid-Finsler metrics form an important class of singular (y-local)
Finsler metrics. They were introduced by G. S. Asanov [2] in 2006. As the
special case of the general construction Asanov produced singular (y - local)
examples of Landsberg spaces of dimension at least three that are not of
Berwald type. The existence of regular (y - global) Landsberg metrics that are
not of Berwald type is an open problem up to this day; for a detailed
exposition of the so-called unicorn problem in Finsler geometry see D. Bao [3].
  In this paper we are going to characterize the Finsleroid-Finsler metrics as
the solutions of a conformal rigidity problem. We are looking for
(non-Riemannian) Finsler metrics admitting a (non-homothetic) conformal change
such that the mixed curvature tensor of the Berwald connection contracted by
the derivatives of the logarithmic scale function is invariant. We prove that
the solutions of class at least $\mathcal{C}^2$ on the complement of the zero
section are conformal to Finsleroid-Finsler metrics.
