Almost symplectic manifold

In differential geometry, an almost symplectic structure on a differentiable manifold $M$ is a two-form $\omega$ on $M$ that is everywhere non-singular. If in addition $\omega$ is closed then it is a symplectic form.

An almost symplectic manifold is an Sp-structure; requiring $\omega$ to be closed is an integrability condition.

Further reading

Alekseevskii, D.V. (2001) [1994], "Almost-symplectic structure", Encyclopedia of Mathematics, EMS Press