A smooth covector field \(\omega\) is called conservative if line integrals are path independent. That is, for two given curve segments \(\gamma\) and \(\widetilde{\gamma}\) with the same starting and end point we have

\begin{equation*} \int_{\gamma} \omega=\int_{\widetilde{\gamma}} \omega. \end{equation*}

Remark

It is called conservative because for moving particles along a force field the energy should be conserved [1, p.292].

Links Link to heading

conservative is equivalent to exact

References Link to heading

J. Lee, Introduction to Smooth Manifolds. New York ; London: Springer, 2013.