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

TL;DR

This paper investigates conformal vector fields on locally projectively flat $(eta)$-Finsler spaces, establishing conditions under which they are homothetic, and providing explicit solutions, with distinctions between Randers and non-Randers types.

Contribution

It proves that conformal vector fields are homothetic on non-Randers type spaces and characterizes their local solutions, highlighting differences in Randers spaces.

Findings

Conformal vector fields are homothetic in non-Randers spaces.

Explicit local solutions for conformal vector fields are determined.

In Randers spaces, conformal vector fields need not be homothetic.

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.