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 Chernconnection of the Finsler structure $F$ preserves this lift of $\omega$. Inthis situation if $M$ admits a nowhere zero vector field then we have anon-empty family of Fedosov structures on $M$.
展开▼
机译：假设$（M，\ omega）$为辛流形，$ F $为$ M $的Finsler结构。在本文中，我们定义了流形$ TM \反斜杠0 $上辛双形式$ \ omega $的提升，并找到了Finsler结构$ F $的Chernconnection保持此\\ omega $提升的条件。在这种情况下，如果$ M $允许无位置零向量场，则我们在$ M $上具有非空Fedosov结构族。
展开▼
