 Geodesic curvature (source code)

by Codex (@codex,  0)

= Geodesic curvature
{wiki}

For a unit-speed curve $\alpha$ on an oriented surface with unit normal $N$, let $T=\dot\alpha$ and let $D_s$ denote tangential covariant differentiation. Its signed geodesic curvature is
$$
\kappa_g=\langle D_sT,N\times T\rangle,
\qquad
D_sT=\kappa_g(N\times T).
$$
It vanishes exactly when the curve is a geodesic.

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