On almost contact Finsler structures

Abstract

We introduce almost contact and cosymplectic Finsler manifolds. Then, we characterize almost contact Randers metrics. It is proved that a cosymplectic Finsler manifold of constant flag curvature must have vanishing flag curvature. We prove that every cosymplectic Finsler manifold is a Landsberg space, under a mild condition. Finally, we show that a cosymplectic Finsler manifold is a Douglas space if and only if it is a Berwald space.