Almost symplectic manifold

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In differential geometry, an almost symplectic structure on a differentiable manifold M is a two-form ω on M that is everywhere non-singular.[1] If, in addition, ω is closed, then it is a symplectic form.

An almost symplectic manifold is an Sp-structure; requiring ω to be closed is an integrability condition.


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