In differential geometry, an almost symplectic structure on a differentiable manifold M is a twoform ω on M that is everywhere nonsingular.^{[1]} If, in addition, ω is closed, then it is a symplectic form.
An almost symplectic manifold is an Spstructure; requiring ω to be closed is an integrability condition.
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References
 ^ Ramanan, S. (2005), Global calculus, Graduate Studies in Mathematics, 65, Providence, RI: American Mathematical Society, p. 189, ISBN 0821837028, MR 2104612.