Helicoidal surfaces of non-lightlike frontals in Lorentz-Minkowski 3-space

TL;DR

This paper introduces two types of helicoidal surfaces in Lorentz-Minkowski 3-space, analyzing their singularities and conditions under which they become lightcone framed base surfaces.

Contribution

It defines new classes of helicoidal surfaces of non-lightlike frontals and establishes identification theorems for their singularities using cusp criteria.

Findings

Characterization of when helicoidal surfaces become lightcone framed base surfaces

Identification theorems for singular types of helicoidal surfaces

Use of cusp criteria to analyze surface singularities

Abstract

In this paper, we define two types of helicoidal surfaces of non-lightlike frontals in Lorentz-Minkowski 3-space and investigate when they become lightcone framed base surfaces. Moreover, by constructing appropriate diffeomorphic transformations and using the criteria of $(i,j)$-cusps and $(i,j)$-cuspidal edges, we establish identification theorems for the singular types of both 1-type and 2-type helicoidal surfaces on their singular loci.