Some classes of projectively and dually flat Finsler spaces with Randers change

Abstract

In this paper, we consider Randers change of some special $(\alpha ,\beta )-$ metrics. First we find the fundamental metric tensor and Cartan tensor of these Randers changed $(\alpha ,\beta )-$metrics. Next, we establish a general formula for inverse of fundamental metric tensors of these metrics. Finally, we find the necessary and sufficient conditions under which the Randers change of these $(\alpha ,\beta )-$ metrics are projectively and locally dually flat.

55 Pages, No figure