Lightlike tangent developables in de Sitter 3-space

Abstract

Developable surfaces are the special ruled surfaces where the Gaussian curvature of each point vanishes. Tangent developable is the most interesting surface among three fundamental types of developable surfaces. This paper investigates lightlike tangent developable generated by a lightlike base curve in de Sitter 3-space. We first give the topological classification of the lightlike curves which lie in de Sitter 3-space by using the theory of finite determinacy. Furthermore, we establish the relationships between lightlike tangent developables and topological types of lightlike curves, and we give the classification of singularities of lightlike tangent developables from the viewpoint of Legendrian singularity theory. Finally, we provide several examples to illustrate our theoretical results.