The relation between parameter curves and lines of curvature on canal   surfaces
  A canal surface is the envelope of a moving sphere with varying radius, defined by the trajectory C(t) (spine curve) of its center and a radius function r(t). In this paper, we investigate when parameter curves of the canal surface are also lines of curvature. Last of all, for special spine curves we obtain the radius function of canal surfaces. 
Fatih Dogan and Yusuf Yayli
math.DG