Construction of curve pairs and their applications

TL;DR

This paper presents a novel approach to constructing and analyzing curve pairs using integral curves, offering new methods for generating partner curves and exploring their applications in various geometric contexts.

Contribution

It introduces new techniques for constructing partner curves of a unit speed curve and explores their applications to helices, slant helices, and plane curves.

Findings

New methods for constructing involute-evolute, Mannheim, and Bertrand curves

Applications to helices, slant helices, and plane curves

Enhanced understanding of curve pair relationships

Abstract

In this study, we introduce a new approach to curve pairs by using integral curves. We consider the direction curve and donor curve to study 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 curve and give some applications related to helices, slant helices and plane curves.