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 $\ne$ 0 are constants) and a Matsumoto metric $\bar{F}=\frac{{\bar{\alpha }}^2}{\bar{\alpha }-\bar{\beta }}$ on a manifold with dimension $n\ge 3$ 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.

16 pages, no figure