On conformal transformations between two (α,β)(α,β)-metrics

In this paper, we characterize the conformal transformations between two (α,β)(α,β)-metrics. Suppose that F   is an (α,β)(α,β)-metric of non-Randers type and is conformally related to F˜, that is, F˜=eκ(x)F, where κ:=κ(x)κ:=κ(x) is a scalar function on the manifold. We prove that, if F   is a Douglas metric, then F˜ is also a Douglas metric if and only if the conformal transformation is a homothety. Further, we prove that, if F is of isotropic S  -curvature, then F˜ is also of isotropic S-curvature if and only if the conformal transformation is a homothety.