Closed differential one-form
= Closed differential one-form
{title2=$\eta\in\Omega^1(M),\quad d\eta=0$}
A <differential one-form> is closed when its <exterior derivative> vanishes. In coordinates, $\eta=\eta_i dx^i$ is closed exactly when $\partial_i\eta_j=\partial_j\eta_i$. The <Poincare lemma> makes it locally an <exact differential form>, but global exactness can fail through nonzero integrals around closed curves.