A smooth covector field is called exact is a smooth function \(f\colon M\to \mathbb{R}\) exists such that
\begin{equation*} \omega=df. \end{equation*}We call \(f\) a potential for \(\omega\).
Remarks
- exact covector fields are especially interesting because of fundamental theorem for line integrals
- not every covector field is exact [@lee2013smooth_manifolds, Example 11.36]