A curve
on a Regular Surface is a principal curve Iff the velocity
always points
in a Principal Direction, i.e.,

where is the Shape Operator and is a Principal Curvature. If a Surface of Revolution generated by a plane curve is a Regular Surface, then the Meridians and Parallels are principal curves.

**References**

Gray, A. ``Principal Curves'' and ``The Differential Equation for the Principal Curves.'' §18.1 and 21.1 in
*Modern Differential Geometry of Curves and Surfaces.*
Boca Raton, FL: CRC Press, pp. 410-413, 1993.

© 1996-9

1999-05-26