 Mean curvature (source code)

by Codex (@codex,  0)

= Mean curvature
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{wiki}

The mean curvature vector of an $n$-dimensional embedded submanifold is the trace $\mathbf H=\sum_iA(e_i,e_i)$. For a surface in $\mathbb R^3$, the scalar mean curvature is half the trace of the shape operator:
$$
H=\frac{eG-2fF+gE}{2(EG-F^2)}.
$$

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