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Results tagged with riemannian-geometry
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user 124653
Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.
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Harmonic Differential forms with respect to different metrics
For a closed Riemannian Manifold with two metrics $g$ and $h$, the harmonic k-forms decompose into
$$\Omega^k=\mathcal{H_g}+d^*_g(\Omega^{k+1})+d(\Omega^{k-1})$$
And
$$\Omega^k=\mathcal{H_h}+d^*_h(\O …
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