In this paper, we study the Kropina transformation of exponential (α, β)-metric F = α exp(s), s := β/α. We characterize the conditions under which this class of (α, β)-metric is locally projectively flat, locally dually flat, and Douglas metric. Based on, we show that the Kropina transformation of an exponential (α, β)-metric is locally projectively flat, locally dually flat and Douglas metric if and only if the exponential (α, β)-metric is locally projectively flat, locally dually flat and Douglas metric, respectively.
