Exact Differential Form

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

A smooth differential \(k\)-form \(\omega\) is called exact if a smooth differential \((k-1)\)-form \(\eta\) exists, such that

\begin{equation*} \omega=d\eta, \end{equation*}

where \(d\eta\) denotes the exterior derivative of \(\eta\).