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

Abstract

The notion of a Douglas space of second kind of a Finsler space with $(\alpha ,\beta )$-metric was introduced by I. Y. Lee [9]. Since then, so many geometers have studied this topic e. g., [14]. In this paper, we prove that a Douglas space of second kind with special -metric $\alpha +\epsilon \beta +k\frac{{\beta }^2}{\alpha }$ is conformally transformed to a Douglas space of second kind. Further, we obtain some results which prove that a Douglas space of second kind with certain $(\alpha ,\beta )$-metrics such as Randers metric, Kropina metric, first approximate Matsumoto metric and Finsler space with square metric is conformally transformed to a Douglas space of second kind.

13 pages