Sweeping surfaces with Natural mate curve of a spatial curve in Euclidean 3-Space

Abstract

In this paper, we introduce the notion of sweeping surfaces with Natural mate curve of a spatial curve in Euclidean 3-space E3 . We also show that the parametric curves on these surfaces are lines of curvature. Then, we derive the necessary and sufficient condition for the sweeping surface to become a developable ruled surface. In particular, we analyze the necessary and sufficient conditions when the resulting developable surface is a cylinder, cone or tangent surface. Finally, some representative curves are chosen to construct the corresponding developable surfaces which possessing these curves as lines of curvature.