> [!definition] > > Let $X$ be a [[Smooth Manifold|smooth manifold]]. A [[Covector Field|covector field]] $\omega \in \vf^*(X)$ is **exact** if there exists a [[Function on Manifold|function]] $f \in C^\infty(X)$ such that $\omega = df$. In which case, $f$ is the **potential** for $\omega$.