This paper is devoted to study of a class of conformally flat (alpha,beta)-metrics that have of the form F=exp(2s)/s; where s:=beta/alpha. They are called Kropina change of exponential (alpha,beta )-metrics. We prove that if F has relatively isotropic mean Landsberg curvature or almost vanishing Xi-curvature then it is a Riemannian metric or a locally Minkowski metric. Also, we prove that, if F be a weak Einstein metric, then it is either a Riemannian metric or a locally Minkowski metric.
