The geometry of lightlike surfaces in Minkowski space

Abstract

We investigate the geometric properties of lightlike surfaces in the Minkowski space ${\mathbb{R}}^{2,1}$, using Cartan's method of moving frames to compute a complete set of local invariants for such surfaces. Using these invariants, we give a complete local classification of lightlike surfaces of constant type in ${\mathbb{R}}^{2,1}$ and construct new examples of such surfaces.