Some Characterizations of Mannheim Partner Curves in Minkowski 3-space

TL;DR

This paper characterizes Mannheim partner curves in Minkowski 3-space, classifies them, explores their relationships, and shows the Mannheim theorem does not hold in this setting, introducing new curvature and torsion relations.

Contribution

It provides the first classification and characterization of Mannheim partner curves in Minkowski 3-space, including new curvature and torsion relationships.

Findings

Mannheim theorem is invalid in Minkowski 3-space.

Classification of Mannheim partner curves established.

New relationships between curvatures and torsions derived.

Abstract

In this paper, we give the characterizations of Mannheim Partner Curves in Minkowski 3-space . Firstly, we classify these curves in . Next, we give some relationships characterizing these curves and we show that Mannheim theorem is not valid for Mannheim partner curves in . Moreover, by considering the spherical indicatrix of the Fr\'enet vectors of those curves, we obtain some new relationships between the curvatures and torsions of the Mannheim partner curves in .