ABSTRACT
A surface can be thought of as being generated by sweeping a flexible curve through space. Then the family of curves as well as the trajectories of their points provides a parametric system. Any curve on such a surface has properties which depend on the surface. In particular, there are curve properties which depend merely on the intrinsic measurements of the sur face. For instance, geodesics are completely defined in terms of the intrinsic surface geometry. Other curve properties depend on the curvature of the surface in space, e.g., lines of curvature have such properties. Again, the analysis rests crucially on the use of a local frame.
