Harmonic one-form
= Harmonic one-form
{title2=$\mathcal H^1(M)$}
A harmonic one-form is a <differential one-form> $\alpha$ satisfying $\Delta\alpha=0$ for the <Hodge Laplacian>. On a <closed manifold>, the <Hodge decomposition theorem> identifies these forms with degree-one <de Rham cohomology>. The <Bochner-Weitzenbock formula for one-forms> implies that <harmonic one-forms are parallel under nonnegative Ricci curvature>.