Time-Like Sweeping Surfaces with a Bishop Frame in the Minkowski 3-Space E 1 3

Abstract

In this paper, we consider a time-like sweeping surface and its local singularities with Bishop frame in Minkowski 3-space E 1 3 . Subsequently, we derive the sufficient and necessary conditions for this surface to be spacelike developable ruled surface. In particular, we mainly focus on the study for the resulting spacelike developable surface is a cylinder, cone or tangent surface. Finally, some representative curves are chosen to construct the corresponding spacelike developable surfaces.