Special projective Lichnérowicz–Obata theorem for Randers spaces

Abstract

It is proved that either every special projective vector field V on a Randers space (M,F=α+β) is a conformal vector field of the Riemannian metric α2−β2, or F is of isotropic S-curvature. This result is applied to establish a projective Lichnérowicz–Obata-type result on the closed manifolds with generic Randers metrics.