Abstract: In this article, we have considered conformal change of Matsumoto Randers transformation of mth -root metric. Furthermore, we have obtained the condition of projectively flatness, projectively dualy flatness with homothetic change and projective factor for said metric. We have also given some fruitful applications of flatness of metric.


Key words: Projectively flatness, projectively dually flatness, mth -root metric, Matsumoto Randers Conformal transformation.