\[ \newcommand{\d}{\mathrm{d}} \newcommand{\e}{\mathrm{e}} \newcommand{\i}{\mathrm{i}} \]

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 \(\omega\).

See also Link to heading

• conservative is equivalent to exact
• every exact covector field is closed
• pullback of exact covector fields is exact