On Kropina transformation of exponential (α,β)-metrics

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.

On Kropina transformation of exponential (α,β)-metrics Keywords:

Locally projectively flat‎ , ‎Locally dually flat‎ , ‎Douglas metric‎ , ‎(α , β)-metric