Special non-lightlike ruled surfaces in Minkowski 3-space

Abstract

In this paper, we give the existence and uniqueness theorems for non-lightlike framed surfaces and define a special non-lightlike ruled surface in Minkowski 3-space. It may have singularities. We give the conditions for identifying cross-caps and surfaces as developable and maximal. Besides, we demonstrate that if the spacelike ruled surface is developable, then the z-parameter curve is an asymptotic curve if and only if the ruled surface is maximal.

Keywords

• non-lightlike framed surface
• cross-cap
• developable surface
• maximal surface
• asymptotic curve