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

A covector field \(\omega\) can be considered as a \(n-1\)-dimensional hyperplane which parallel to \(\ker \omega\). I.e. a covector field with small values is a hyperplane which is far away from its origin.