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Almost symplectic manifold

## Summary

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

1. ^ Ramanan, S. (2005), Global calculus, Graduate Studies in Mathematics, vol. 65, Providence, RI: American Mathematical Society, p. 189, ISBN 0-8218-3702-8, MR 2104612.