Almost symplectic manifold

In differential geometry, an almost symplectic structure on a differentiable manifold ${\displaystyle M}$ is a two-form ${\displaystyle \omega }$ on ${\displaystyle M}$ that is everywhere non-singular.^[1] If in addition ${\displaystyle \omega }$ is closed then it is a symplectic form.

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