SPECIAL PROJECTIVE ALGEBRA OF RANDERS METRICS OF CONSTANT S-CURVATURE

Abstract

The collection of all projective vector fields on a Finsler space (M, F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra. A specific Lie sub-algebra of projective algebra of Randers spaces (called the special projective algebra) of non-zero constant S-curvature is studied and it is proved that its dimension is at most [Formula: see text]. Moreover, a local characterization of Randers spaces whose special projective algebra has maximum dimension is established. The results uncover somehow the complexity of projective Finsler geometry versus Riemannian geometry.