Conformal Vector Fields On Projectively Flat $(\alpha ,\beta )$-Finsler Spaces

Abstract

In this paper, it is proved that any conformal vector field is homothetic on a locally projectively flat $(\alpha ,\beta )$-space of non-Randers type in dimension $n\ge 3$, and the local solutions of such a vector field are determined. While on a locally projectively flat Randers space, examples showthat the conformal vector fields are not necessarily homothetic.

12 pages