What is Contact type?

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