Lorentzian Darboux images of curves on spacelike surfaces in Lorentz-Minkowski 3-space

TL;DR

This paper studies the Lorentzian Darboux frames of curves on spacelike surfaces in Lorentz-Minkowski 3-space, introducing special vector fields and analyzing their singularities to deepen understanding of their geometric properties.

Contribution

It introduces five new vector fields associated with Lorentzian Darboux frames and investigates their singularities, advancing the geometric analysis of curves on spacelike surfaces.

Findings

Identification of five special vector fields along the curve

Analysis of singularities of these vector fields

Enhanced understanding of Lorentzian Darboux frames in Lorentz-Minkowski space

Abstract

For a regular curve on a spacelike surface in Lorentz-Minkowski $3$-space, we have a moving frame along the curve which is called a Lorentzian Darboux frame. We introduce five special vector fields along the curve associated to the Lorentzian Darboux frame and investigate their singularities.