Contact type

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