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.

References

Further reading

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

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