In
differential geometry, an almost symplectic structure on a
differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One ma ...
is a
two-form on
that is everywhere non-singular.
[.] If in addition
is
closed then it is a
symplectic form In mathematics, a symplectic vector space is a vector space ''V'' over a field ''F'' (for example the real numbers R) equipped with a symplectic bilinear form.
A symplectic bilinear form is a mapping that is
; Bilinear: Linear in each argument ...
.
An almost symplectic manifold is an
Sp-structure; requiring
to be closed is an
integrability condition In mathematics, certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of a system of differential forms. The idea is to take advantage of t ...
.
References
{{differential-geometry-stub
Smooth manifolds
Symplectic geometry