Symplectization

In mathematics, the symplectization of a contact manifold is a symplectic manifold which naturally corresponds to it.

Consider the set of all nonzero 1-forms at

, which have the contact plane

The union is a symplectic submanifold of the cotangent bundle of

, and thus possesses a natural symplectic structure.

supplies the symplectization with the structure of a principal bundle over

with structure group

is cooriented by means of a contact form

, there is another version of symplectization, in which only forms giving the same coorientation to

Any section of this bundle is a coorienting form for the contact structure.