Lightlike surfaces with planar normal sections in Minkowski 3-space

TL;DR

This paper investigates lightlike surfaces in Minkowski 3-space, demonstrating that all have degenerate planar normal sections and characterizing those with non-degenerate planar normal sections.

Contribution

It provides a complete classification of lightlike surfaces with planar normal sections in Minkowski 3-space, including the first characterization of non-degenerate cases.

Findings

All lightlike surfaces in Minkowski 3-space have degenerate planar normal sections.

Characterization of lightlike surfaces with non-degenerate planar normal sections.

Established conditions for the existence of non-degenerate planar normal sections.

Abstract

In this paper we study lightlike surfaces of Minkowski 3- space such that they have degenerate or non-degenerate planar normal sections. We first show that every lightlike surface of Minkowski $3-$ space has degenerate planar normal sections. Then we study lightlike surfaces with non-degenerate planar normal sections and obtain a characterization for such lightlike surfaces.