Some Characterizations of slant and spherical helices in Minkonwski 3-space

TL;DR

This paper investigates conditions on geodesic curvature of curves on specific surfaces in Minkowski space to determine when these curves form spherical or slant helices, contributing to the geometric understanding of such curves.

Contribution

It provides new characterizations of when curves derived from geodesics on certain surfaces are spherical or slant helices in Minkowski space.

Findings

Conditions on geodesic curvature for spherical helices

Conditions on geodesic curvature for slant helices

Characterizations of curves on $S_1^2$ and $H_0^2$ in Minkowski space

Abstract

In this paper, we are investigating that under which conditions of the geodesic curvature of unit speed curve $\gamma$ that lies on $S_1^2$ or $H_0^2$, the curve $\alpha$ which is obtained by using $\gamma$, is a spherical helix or slant helix in Minkowski space.