In differential geometry, an almost symplectic structure on a differentiable manifold is a two-form on that is everywhere non-singular.[1] If in addition is closed then it is a symplectic form.
An almost symplectic manifold is an Sp-structure; requiring to be closed is an integrability condition.
Alekseevskii, D.V. (2001) [1994], "Almost-symplectic structure", Encyclopedia of Mathematics, EMS Press