Let $Q$ be a smooth $n$-manifold, let $S\in C^\infty(Q;\mathbb R)$, and let $T^*Q$ carry its tautological one-form $\lambda\in\Omega^1(T^*Q)$ and canonical symplectic form $\omega_{\mathrm{can}}=-d\lambda$. Define the smooth section
be its graph. Then $\Gamma_{dS}$ is a Lagrangian submanifold of $(T^*Q,\omega_{\mathrm{can}})$. Moreover, under the identification $Q\cong \Gamma_{dS}$ given by $i_{dS}$, the restricted tautological one-form is $dS$: