ABSTRACT
In this chapter we continue our study of special curves on surfaces. A principal curve on a surface is a curve whose velocity always points in a principal direction, that is, a direction in which the normal curvature is a maximum or a minimum. In Section 19.1, we derive the differential equation for the principal curves on a patch in ℝ3 and give examples of its solution. As in Section 18.2, the idea then is to reparametrize a surface with specified coordinate curves.
