  Let $(M,\omega)$ be a symplectic manifold and $F$ be a Finsler structure on
$M$. In the present paper we define a lift of the symplectic two-form $\omega$
on the manifold $TM\backslash 0$, and find the conditions that the Chern
connection of the Finsler structure $F$ preserves this lift of $\omega$. In
this situation if $M$ admits a nowhere zero vector field then we have a
non-empty family of Fedosov structures on $M$.

Differential Geometry