Spacelike Sweeping Surfaces and Singularities in Minkowski 3-Space

Abstract

We considered the spacelike sweeping surface with rotation minimizing frames at Minkowski 3-space ${\mathbb{E}}_1^3$ . We presented the new geometric invariant to demonstrate geometric properties and local singularities for this surface. Then, we derived sufficient and necessary conditions of the surface to become developable ruled surfaces. Additionally, its singularities are studied. Finally, examples are illustrated to explain the applications of the theoretical results.