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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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Intuition for the Drift Term of the Laplace-Beltrami Operator

In coordinates, the Laplace-Beltrami operator on a Riemannian manifold $(M,g)$ can be written as: $$ \Delta_g = g^{ij}\partial_{ij} - g^{jk}\Gamma^\ell_{jk}\partial_\ell $$ The second term: $$ \mu^\el …
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