On the conformal change of a Douglas space of a second kind with a class of ($\alpha, \beta $)-metric

Abstract

In the present work, we study the special $ (\alpha, \beta) $-metric as a generalization of second approximation of infinite series $ (\alpha, \beta) $-metric. By applying the Chern and Shen's Lemma, we have derived the conditions for this special $ (\alpha, \beta)-$metric to be considered a Finsler metric. Additionally, we assert that under specific circumstances, the resulting space is classified as a Douglas space. Moreover, we have identified the conditions under which a Douglas space of the second kind, equipped with this metric, can be conformally transformed into another Douglas space of the second kind.