Projective Change between Randers Metric and Special $(α, β)$-metric (Journal of Informatics and Mathematical Sciences, 2012)
In the present paper, we find the conditions to characterize projective change between two $(α, β)$-metrics, such as special $(α, β)$-metric, $L=α-\frac{β^2}{α}+β$ and Randers metric $\bar{L}= \bar{α}+\bar{β}$ on a manifold with dim $n ≥ 3$, where $α$ and $\bar{α}$ are two Riemannian metrics, $β$ and $\bar{β}$ are two non-zero 1-forms. Further, we study the special curvature properties of two classes of $(α, β)$-metrics.
Keywords: Projective change; Randers metric; Douglas metric; Projective invariant; Locally Minkowski space