Green operator of the Hodge Laplacian
= Green operator of the Hodge Laplacian
{c}
{title2=$G$}
On a compact oriented <Riemannian manifold>, the Green operator $G$ is the inverse of the <Hodge Laplacian> on the orthogonal complement of harmonic forms and is zero on harmonic forms. If $H$ is harmonic projection, then
$$
\Delta G=G\Delta=1-H.
$$
It commutes with every differential operator that commutes with $\Delta$.