Coisotropic submanifold

A coisotropic submanifold $N$ satisfies $(T_{p}N{)}^{\omega }\subset T_{p}N$, where the superscript denotes the symplectic orthogonal complement. Every hypersurface of a symplectic manifold is coisotropic.

For a hypersurface $N$ of a symplectic manifold, the restriction of the symplectic form has a one-dimensional kernel, its characteristic line field. On a regular value level $N=H^{-1}(c)$, this line is generated by the Hamiltonian vector field of $H$.