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Diffgeom β

Laplace-Beltrami operator

This is a variation of Laplacian

Definition

The Laplace-Beltrami operator is a second-order differential operator from the sheaf of functions on a Riemannian manifold (or more generally, a pseudo-Riemannian manifold) to itself. The Laplace-Beltrami operator is defined by taking a divergence of a gradient, where both these are defined in terms of the Riemannian or pseudo-Riemannian structure:

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