Projective changes between two Finsler spaces with $(\alpha, \beta )$-metrics

Abstract

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