Conformal transformation of Douglas space of second kind with special (α, β)-metric

Abstract

PurposeIn this paper, the authors prove that the Douglas space of second kind with a generalised form of special (α, β)-metric F, is conformally invariant.Design/methodology/approachFor, the authors have used the notion of conformal transformation and Douglas space.FindingsThe authors found some results to show that the Douglas space of second kind with certain (α, β)-metrics such as Randers metric, first approximate Matsumoto metric along with some special (α, β)-metrics, is invariant under a conformal change.Originality/valueThe authors introduced Douglas space of second kind and established conditions under which it can be transformed to a Douglas space of second kind.