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Results tagged with smooth-manifolds
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user 102881
Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].
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answers
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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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