For a unit speed curve on a surface, the length of the surface-tangential component of acceleration is the geodesic curvature . Curves with are called Geodesics. For a curve parameterized as , the geodesic curvature is given by
See also Geodesic
Gray, A. ``Geodesic Curvature.'' §20.5 in
Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press,
pp. 402-407, 1993.