Just as the zero section in $T^*\mathbb{R}^N$ (equipped with the standard symplectic form) is the "model" / "quintessential" Lagrangian submanifold, does $T^*\mathbb{R}^N$ have a "model" coisotropic submanifold?

Let $(M, \Omega)$ be a presymplectic manifold and let $E \longrightarrow M$ be the characteristic bundle of $(M, \Omega)$, defined fiberwise by $$E_x = \{v \in T_x M : \Omega_x(v, ) = 0\}.$$ If $E^\ast$ denotes the dual bundle to $E$, then we have the following classification theorem.
The presymplectic form $\Omega$ specifies what the pullback of $\omega$ to $M$ is. For a Lagrangian embedding, $\Omega \equiv 0$ and hence $E^\ast = T^\ast M$, and we recover the fact that the zero section of $T^\ast M$ is the canonical model for a Lagrangian embedding of $M$ into a symplectic manifold. For the details, see the original paper of Gotay:


