Sruthy Asha Baby | Searcharxiv

arXiv2018

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

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 $α+εβ+ k \frac{β^2}{α}$ 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.

math.DG↗

arXiv2017

Projective changes between two Finsler spaces with $(α, β)$-metrics

In the present paper, we find the conditions to characterize projective change between two $(α, β)$-metrics, F = $α+ εβ+ k\frac{β^2}α$ ($ε$ and k $\neq$ 0 are constants) and a Matsumoto metric $\bar{F}=\frac{\barα^2}{\barα -\barβ}$ on a manifold with dimension $n \geq 3$ where $α$ and $\barα$ are two Riemannian metrics, $β$ and $\barβ$ are two non-zero 1-forms. Moreover, we study such projective changes when F has some special curvature properties.

math.DG↗