Relatively normal-slant helices in Minkowski $3$-space

TL;DR

This paper investigates the properties and characterizations of relatively normal-slant helices on timelike and spacelike surfaces in Minkowski 3-space, establishing their axes via Darboux frames and exploring their relation to slant helices.

Contribution

It introduces new characterization theorems for relatively normal-slant helices in Minkowski 3-space and analyzes their axes and relationships to other helices.

Findings

Axes of helices obtained via Darboux frames

Characterization theorems for spacelike and timelike helices

Relationship between relatively normal-slant and slant helices

Abstract

In this paper, we study relatively normal-slant helices lying on timelike as well as spacelike surfaces in Minkowski $3$-space $ \mathbb{E}_1^3$. The axes of spacelike and timelike relatively normal-slant helices are obtained via their Darboux frames. We also establish characterization theorems for spacelike and timelike relatively normal-slant helices in Minkowski $3$-space $\mathbb{E}_1^3$. Finally, the relationship between relatively normal-slant helices and slant helices is found on timelike as well as spacelike surfaces.