On the conformal change of a Douglas space of a second kind with a class of (α, β)-metric

Renu, R. S. Kushwaha

In the present work, we study the special (α, β)-metric as a generalization of second approximation of infinite series (α, β)-metric. By applying the Chern and Shen's Lemma, we have derived the conditions for this special (α, β)-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. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 17(2) (2024), pp. 123-135