Geodesic Curvature
For a unit speed curve on a surface, the length of the surface-tangential component of acceleration is the geodesiccurvature 
. Curves with 
are called Geodesics. For a curve parameterizedas 
, the geodesic curvature is given by
where
, 
, and 
are coefficients of the first Fundamental Form and 
are Christoffel Symbols of the Second Kind.See also Geodesic
References
Gray, A. ``Geodesic Curvature.'' §20.5 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 402-407, 1993.
- Birthday Attack
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