Let $M$ be a [smooth manifold](/page/Smooth%20Manifold), let $U\subset M$ be an open subset, and let $(\omega_t)_{t\in[0,1]}$ be a smooth one-parameter family of symplectic forms on $U$. Suppose there is a smooth one-parameter family $(\sigma_t)_{t\in[0,1]}$ of $1$-forms on $U$ such that