Smooth Differential Form

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

A diffenrential form is called smooth if it is a smooth tensor field . The set of smooth differential \(k\)-forms is denoted by

\begin{equation*} \Omega^k(M)=\Gamma(\Lambda^kT^*M). \end{equation*}