Contact type

In mathematics, more precisely in symplectic geometry, a hypersurface $$\Sigma $$ of a symplectic manifold $$(M,\omega)$$ is said to be of contact type if there is 1-form $$\alpha$$ such that $$j^{*}(\omega)=d\alpha$$ and $$(\Sigma,\alpha)$$ is a contact manifold, where $$ j: \Sigma \to M $$ is the natural inclusion. The terminology was first coined by Alan Weinstein.