The Randers changes of Finsler spaces with \((\alpha,\beta)\)-metrics of Douglas type (Q2731051)

A change \(\overline L= L(x,y)+\rho(x,y)\), \(\rho= \rho_i(x)y^i\), of a Finsler metric \(L\) is called a Randers change. In particular, a change \(\overline L= L(\alpha,\beta)+ \beta\) of an \((\alpha,\beta)\)-metric \(L(\alpha,\beta)\) is called special. Among other theorems we have the following: A Finsler space \(\overline F^n\) \((n>2)\) which is obtained by a special Randers change of a Kropina space \(F^n\) with \(b^2\neq 0\) is of Douglas type, iff \(F^n\) is of Douglas type.