Journal of the
Korean Mathematical Society JKMS

A change of Finsler metric $L(x, y) \longrightarrow \overline L(x,y)$ is called a Randers change of $L$, if $\overline L(x, y) = L(x, y) + \rho (x,y)$, where $\rho (x,y) = \rho _i(x)y^i$ is a $1$-form on a smooth manifold $M^n$. Let us consider the special Randers change of Finsler metric $L \longrightarrow \overline L=L+\beta$ by $\beta$. On the basis of this special Randers change, the purpose of the present paper is devoted to studying the conditions for Finsler space $\overline{F}^n$ which are transformed by a special Randers change of Finsler spaces $F^n$ with $(\alpha, \beta)$-metrics of Douglas type to be also of Douglas type, and vice versa.

Keywords: Douglas space, Finsler metric, homogeneous polynomials, Randers change, special Randers change

MSC numbers: 53B40