Special involute-evolute partner D-curves in E3

TL;DR

This paper studies special involute-evolute partner D-curves on surfaces in three-dimensional space, analyzing their Darboux frames and curvature relations, and providing examples and consequences of these geometric properties.

Contribution

It introduces a new class of involute-evolute partner D-curves on surfaces in E3 and explores their curvature relationships and geometric properties.

Findings

Relations between normal, geodesic curvatures, and torsions are established.

Examples illustrating the properties of these curves are provided.

Theoretical consequences of the curvature relations are discussed.

Abstract

In this paper, we take into account the opinion of involute-evolute curves which lie on fully surfaces and by taking into account the Darboux frames of them we illustrate these curves as special involute-evolute partner D-curves in E3. Besides, we find the relations between the normal curvatures, the geodesic curvatures and the geodesic torsions of these curves. Finally, some consequences and examples are given.