Some Properties of Mannheim Curves in Galilean and Pseudo - Galilean space

TL;DR

This paper investigates Mannheim curves within 3D Galilean and Pseudo-Galilean spaces, deriving relationships between their curvatures and torsions to understand their geometric properties.

Contribution

It provides new characterizations of Mannheim partner curves in non-Euclidean geometries, expanding the understanding of their curvature and torsion relationships.

Findings

Derived curvature-torsion relationships for Mannheim curves in Galilean space.

Established characterizations of Mannheim curves in Pseudo-Galilean space.

Enhanced geometric understanding of Mannheim curves in non-Euclidean contexts.

Abstract

The aim of this work is to study the Mannheim curves in 3-dimensional Galilean and Pseudo - Galilean space. We obtain the characterizations between the curvatures and torsions of the Mannheim partner curves.