Geodesic curvature

Summary

The geodesic curvature of a curve on a surface measures how much the curve bends within the surface. The acceleration of a unit-speed curve on a surface splits into a part normal to the surface and a part tangent to it. The geodesic curvature is the size of the tangent part, with a sign. Curves with geodesic curvature zero are the geodesics, the straightest curves of the surface. It is intrinsic: it depends only on the first fundamental form.