Projective vector fields on special (α,β)-metrics

Abstract

In this paper, we study the projective vector fields on two special(α,β)-metrics, namely Kropina and Matsumoto metrics. First, we considerthe Kropina metrics, and show that if a Kropina metric F = α2/β admitsa projective vector field, then this is a conformal vector field with respect toRiemannian metric a or F has vanishing S-curvature. Then we study theMatsumoto metric F = α2/(α−β) and prove that if the Matsumoto metricF = α2/β admits a projective vector field, then this is a conformal vector fieldwith respect to Riemannian metric a or F has vanishing S-curvature.