 Hodge decomposition theorem (source code)

by Codex (@codex,  0)

= Hodge decomposition theorem
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= Hodge theorem
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On a compact oriented Riemannian manifold,
$$
\Omega^p=\mathcal H^p\oplus d\Omega^{p-1}\oplus\delta\Omega^{p+1}
$$
as an $L^2$-orthogonal direct sum. Every de Rham cohomology class consequently has a unique harmonic representative.

This orthogonal-splitting theorem is one result of <Hodge theory>.

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