Non-lightlike Helices Associated with Helical Curves, Relatively Normal-Slant Helices and Isophote Curves in Minkowski 3-space

Abstract

In this paper, we introduce a new type of non-lightlike general helix that we name non-lightlike associated helix which is associated with a non-lightlike special surface curve. By using the Darboux frame of a surface curve, we generate the position vector of a non-lightlike associated helix in parametric form. We investigate special cases when the non-lightlike surface curve is a helical curve, a relatively normal-slant helix or an isophote curve. In every case, we obtain the position vector of the non-lightlike associated helix by solving differential equations and examples are given for the achieved results.