Lightlike sweeping surface and singularities in Minkowski 3–space E₃¹

In this work, we give the parametric equation of a lightlike sweeping surface in Minkowski 3–Space (Formula presented). We introduce a new geometric invariant to explain the geometric possessions and local singularities of this lightlike sweeping surface. We extract the sufficient and necessary conditions for this lightlike sweeping surface to be a spacelike/timelike developable ruled surface. Afterwards, we take advantage of singularity theory to give the categorization of singularities of this spacelike/timelike developable surface. Finally, we give several representative examples to offer the implementations of the theoretical results.