Coclosed differential form
= Coclosed differential form
{title2=$\delta\alpha=0$}
A <differential form> is coclosed when its <codifferential> vanishes. On a closed <Riemannian manifold>, a form is a <harmonic differential form> exactly when it is both a <closed differential form> and coclosed: the identity $\langle\Delta\alpha,\alpha\rangle=\|d\alpha\|^2+\|\delta\alpha\|^2$ proves the converse as well as necessity.