Twisted Lagrangian graph criterion
= Twisted Lagrangian graph criterion
{title2=$\theta^*\omega_\sigma=\sigma-d\theta$}
With $\omega=-d\alpha$ and $\omega_\sigma=\omega+\pi^*\sigma$, the <one-form graph> of $\theta$ is a <Lagrangian submanifold> exactly when $d\theta=\sigma$. Indeed its pulled-back <symplectic form> is $\sigma-d\theta$ and its dimension is half that of the total space. This extends <graph of a closed one-form is Lagrangian>.