# Laplace-Beltrami operator

From Diffgeom

*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:

*Fill this in later*