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Differential form

Hodge star operator

Harmonic differential form

{c}
{wiki=Hodge_theory#Hodge_decomposition}

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.


Hodge decomposition theorem

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 131 / 3 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 131 / 3 / c / Solution

Hodge decomposition theorem

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Hodge decomposition theorem

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