Almost symplectic manifold
From HandWiki
In differential geometry, an almost symplectic structure on a differentiable manifold [math]\displaystyle{ M }[/math] is a two-form [math]\displaystyle{ \omega }[/math] on [math]\displaystyle{ M }[/math] that is everywhere non-singular.[1] If in addition [math]\displaystyle{ \omega }[/math] is closed then it is a symplectic form. An almost symplectic manifold is an Sp-structure; requiring [math]\displaystyle{ \omega }[/math] to be closed is an integrability condition.
References
- ↑ Ramanan, S. (2005), Global calculus, Graduate Studies in Mathematics, 65, Providence, RI: American Mathematical Society, p. 189, ISBN 0-8218-3702-8, https://books.google.com/books?id=1INoRKtgndcC&pg=PA189.
Further reading
Hazewinkel, Michiel, ed. (2001), "Almost-symplectic structure", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=Main_Page
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