nLab symplectic connection

Definition

An affine connection $\nabla$ on a symplectic manifold $(X,\omega)$ is a symplectic connection if the symplectic form is covariantly constant with respect to the connection, $\nabla \omega = 0$.

Applications

In deformation quantization

The second order term in the formal deformation quantization (see there) of a symplectic manifold is closely related to symplectic connections.

References

• eom, Symplectic connection