Bertrand Partner D-Curves in Minkowski 3-space

TL;DR

This paper introduces Bertrand D-curves on surfaces in Minkowski 3-space, characterizing their properties and relations to other curvatures, extending classical Bertrand curve concepts to a Lorentzian setting.

Contribution

It defines Bertrand D-curves using the Darboux frame in Minkowski 3-space and explores their geometric properties and relations, extending classical Bertrand curve theory.

Findings

Characterization of Bertrand D-curves in Minkowski 3-space

Relations between geodesic, normal curvatures, and torsions

Extension of Bertrand curve concepts to Lorentzian geometry

Abstract

In this paper, we consider the idea of Bertrand curves for curves lying on surfaces in Minkowski 3-space. By considering the Darboux frame, we define these curves as Bertrand D-curves and give the characterizations for those 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 in Minkowski 3-space, the definition and the characterizations of Bertrand D-curves include those of Bertrand curves in some special cases.