Some new characterizations of projective Randers metrics with constant S-curvature

Randers metrics are popular Finsler metrics appearing in many physical and geometric studies. A classical result asserts that projective algebra (i.e. the Lie algebra of projective vector fields) of projective nn-dimensional (n≥3)(n≥3) Riemannian metrics has maximum dimension n(n+2)n(n+2) and vice-versa. In this paper, a Lie sub-algebra of projective vector fields of a Finsler metric FF is introduced denoted by SP(F). It is proved that, Randers metric of non-zero constant S-curvature is projective if and only if the dimension of SP(F) is n(n+1)2. Applying this result, it is also proved that a Randers metric of non-zero constant S-curvature is projective if and only if the dimension of the projective algebra equals n(n+2)n(n+2).