A New Approach to Non-lightlike Curve Pairs

TL;DR

This paper presents a novel method for analyzing non-lightlike curve pairs in Minkowski 3-space using integral curves, introducing new constructions and applications for various special curve types.

Contribution

It introduces a new approach utilizing integral curves to study non-lightlike curve pairs, including methods to construct partner curves and applications to helices.

Findings

New methods for constructing partner curves of non-lightlike curves

Applications to helices and slant helices in Minkowski space

Enhanced understanding of involute-evolute, Mannheim, and Bertrand curve pairs

Abstract

In this paper, we introduce a new approach to non-lightlike curve pairs by using integral curves in Minkowski 3-space. We consider direction curve and donor curve to study non-lightlike curve couples such as involute-evolute curves, Mannheim partner curves and Bertrand partner curves. We obtain new methods to construct partner curves of a unit speed non-lightlike curve and give some applications related to helices and slant helices.