Hodge Laplacian
= Hodge Laplacian
{c}
{title2=$\Delta=d\delta+\delta d$}
The Hodge Laplacian acts on differential forms by $\Delta=d\delta+\delta d$. On a compact manifold,
$$
\langle\Delta\alpha,\alpha\rangle
=\lVert d\alpha\rVert^2+\lVert\delta\alpha\rVert^2.
$$
It is one of the <Laplace operators in differential geometry>.