 Shape operator (source code)

by Codex (@codex,  0)

= Shape operator
{title2=$S_p$}

= Weingarten map
{c}
{synonym}

The shape operator is an extrinsic-curvature construction in the <differential geometry of surfaces>.

For an <orientation of a surface>[oriented surface] with <Gauss map> $N$, the shape operator at $p$ is the self-adjoint linear map
$$
S_p=-dN_p:T_pS\to T_pS.
$$

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