Singularities of null surfaces of null Cartan curves in three-dimensional anti-de Sitter space

Abstract

In this paper, we investigate the geometric properties of a kind of null surfaces associated to null Cartan curves in three dimensional anti-de Sitter space from the singularity theory viewpoint. We define a map which is called the binormal height function and introduce two geometric invariants for null Cartan curves. Taking advantage of them, we study the singularities of the null surfaces as applications of singularity theory of functions.