Admissible Mannheim Curves in Pseudo-Galilean Space $G_3^1$

TL;DR

This paper introduces and analyzes admissible Mannheim partner curves in pseudo-Galilean space, establishing their geometric properties, constant distances, torsions, and conditions under which they form general helices.

Contribution

It defines first and second type admissible Mannheim curves in pseudo-Galilean space and derives their key geometric relations and properties, including Schell Theorem and helix conditions.

Findings

Distance between reciprocal points is constant.

Torsions of Mannheim partner curves are constant.

Relations between curvatures and torsions are established.

Abstract

In this paper, first and second type admissible Mannheim partner curves are defined in pseudo-Galilean space $G_3^1$. Moreover, it is proved that the distance between the reciprocal points of both of first and second type admissible Mannheim curves and the torsions of these curves are constant. Furthermore, the relations for curvatures and torsions of these curves and Schell Theorem are obtained. Finally, a result about these curves being general helix is given.