Bertrand Partner D-Curves in Euclidean 3-space

TL;DR

This paper introduces Bertrand D-curves on surfaces in Euclidean 3-space, characterizing their properties via Darboux frames and relating their curvatures and torsions, extending classical Bertrand curve concepts.

Contribution

It defines Bertrand D-curves on surfaces using Darboux frames and provides new characterizations and relations among their geometric invariants.

Findings

Relations between geodesic, normal curvatures, and geodesic torsions of Bertrand D-curves

Characterizations of Bertrand D-curves include classical Bertrand curves as special cases

New geometric properties of curves on surfaces in Euclidean 3-space

Abstract

In this paper we consider the idea of Bertrand curves for curves lying on surfaces and by considering the Darboux frames of them we define these curves as Bertrand D-curves and give the characterizations for these curves. We also find the relations between the geodesic curvatures, the normal curvatures and the geodesic torsions of these associated curves. Furthermore, we show that the definition and the characterizations of Bertrand D-curves include those of Bertrand curves in some special cases.