Conformally related invariant $(\alpha ,\beta )$-metrics on homogeneous spaces

In this paper, we give the flag curvature formula of general $(\alpha ,\beta )$-metrics of Berwald type. We study conformally related $(\alpha ,\beta )$-metrics, especially general $(\alpha ,\beta )$-metrics that are conformally related to invariant $(\alpha ,\beta )$-metrics. Also, a necessary and sufficient condition for a Finsler metric conformally related to an $(\alpha ,\beta )$-metric is given, and conformally related Douglas Randers metrics are studied. Finally, we present some examples of conformally related $(\alpha ,\beta )$-metrics.