On Randers Conformal Transformation of m -th Root Metric

In this paper, we present the theory of Randers conformal transformation of m -th root metric. We find a condition under which Randers conformal transformed m -th root metric is projectively related to m -th root metric. Further, we find a condition for which Randers conformal transformed m -th root metric is locally dually flat and projectively flat. Significant statement: The m-th root metrics are an extension of Riemannian metrics (when m=2 ) which are used in biology as ecological metrics. Recent studies show that m-th root metrics play a very important role in physics, space-time and general relativity as well as in unified gauge field theory. Metric is considered as generalization of the conformal change, (when β =0 ) as well as Randers change, (when σ =0 ) and homothetic change (when β =0 and σ _i=∂α/∂ x^i=0).