Fedosov manifold
In mathematics, a Fedosov manifold is a symplectic manifold with a compatible torsion-free connection, that is, a triple, where is a symplectic manifold, and ∇ is a symplectic torsion-free connection on M. = ω + ω for all vector fields X,Y,Z ∈ Γ Note that every symplectic manifold admits a symplectic torsion-free connection. Cover the manifold with Darboux charts and on each chart define a connection ∇ with Christoffel symbol. Then choose a partition of unity 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.Examples
For example, with the standard symplectic form has the symplectic connection given by the exterior derivative. Hence, is a Fedosov manifold.
