The geometry of lightlike surfaces in Minkowski space

TL;DR

This paper studies the geometric properties of lightlike surfaces in Minkowski space, classifies those of constant type using invariants, and constructs new examples, advancing understanding of their local geometry.

Contribution

It provides a complete local classification of lightlike surfaces of constant type in Minkowski space and introduces new examples using Cartan's method.

Findings

Complete set of local invariants for lightlike surfaces

Classification of constant type lightlike surfaces

Construction of new examples of such surfaces

Abstract

We investigate the geometric properties of lightlike surfaces in the Minkowski space $\R^{2,1}$, 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 $\R^{2,1}$ and construct new examples of such surfaces.