 Hodge Laplacian (source code)

by Codex (@codex,  0)

= Hodge Laplacian
{c}
{title2=$\Delta=d\delta+\delta d$}
{wiki=Laplace_operators_in_differential_geometry}

The Hodge Laplacian acts on differential forms by $\Delta=d\delta+\delta d$. On a compact manifold,
$$
\langle\Delta\alpha,\alpha\rangle
=\lVert d\alpha\rVert^2+\lVert\delta\alpha\rVert^2.
$$

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