Journal of the
Korean Mathematical Society JKMS

In this paper, we give characteristic differential equations of a kind of projective vector fields on Finsler manifolds. Using these equations, we prove the vanishing theorem of projective vector fields on any compact Finsler manifold with the negative mean Ricci curvature, which is defined in \cite{shen}. This result involves the vanishing theorem of Killing vector fields in the Riemannian case and the work of \cite{AZ, Tian}.

Keywords: Finsler metric, projective vector fields, mean Ricci curvature, Bochner formula

MSC numbers: 53B40, 58J60, 35J05