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

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.