is a symplectic form, a non-degenerate closed exterior 2-form, on a
In other words, the symplectic form is parallel with respect to the connection, i.e., its covariant derivative vanishes.)
Cover the manifold with Darboux charts and on each chart define a connection ∇ with Christoffel symbol
Then choose a partition of unity (subordinate to the cover) and glue the local connections together to a global connection which still preserves the symplectic form.
The famous result of Boris Vasilievich Fedosov gives a canonical deformation quantization of a Fedosov manifold.
has the symplectic connection given by the exterior derivative
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