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

Year 2023, Volume: 4 Issue: 2, 107 - 127, 31.07.2023

Onur Kaya

https://doi.org/10.54974/fcmathsci.1246015

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.

Keywords

Non-lightlike associated helix, non-lightlike isophote curve, non-lightlike relatively normal-slant helix

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