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.

中文翻译：

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几乎接触 Finsler 结构

我们介绍了几乎接触和余辛 Finsler 流形。然后，我们描述了几乎接触 Randers 指标。证明了恒旗曲率的余辛 Finsler 流形必然具有消失的旗曲率。我们证明了在温和条件下，每个余辛 Finsler 流形都是 Landsberg 空间。最后，我们证明了余辛 Finsler 流形是道格拉斯空间当且仅当它是 Berwald 空间。