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

2018/06/20 by Shanker, Gauree, Baby, Sruthy Asha
#53B40 #53C60 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.07939

Abstract

The notion of a Douglas space of second kind of a Finsler space with (α, β)-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 % (α, β)-metric α+εβ+ k (β²)/(α) 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 (α, β)-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.

Related

• Douglas metrics of (α,β) type
• On Douglas general (α,β)-metrics
• On general (alpha,beta)-metrics with vanishing Douglas curvature
• On (α, β, γ)-metrics
• On singular square metrics with vanishing Douglas curvature