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

where , , and are coefficients of the first Fundamental Form and are Christoffel Symbols of the Second Kind.

**References**

Gray, A. ``Geodesic Curvature.'' §20.5 in
*Modern Differential Geometry of Curves and Surfaces.* Boca Raton, FL: CRC Press,
pp. 402-407, 1993.

© 1996-9

1999-05-25