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

Abstract

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 n -dimensional ( n ≥ 3 ) Riemannian metrics has maximum dimension n ( n + 2 ) and vice-versa. In this paper, a Lie sub-algebra of projective vector fields of a Finsler metric F 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 ) .