On dual timelike - spacelike Mannheim partner curves in ID3 1

TL;DR

This paper introduces dual timelike-spacelike Mannheim partner curves in Dual Lorentzian Space ID3 1, deriving their curvature and torsion relationships and establishing conditions for their existence.

Contribution

It defines a new class of curves in Dual Lorentzian Space and derives their geometric relationships and necessary conditions for Mannheim partner curves.

Findings

Established the definition of dual timelike-spacelike Mannheim partner curves.

Derived relationships between curvatures and torsions of the curves.

Provided necessary and sufficient conditions for these curves in ID3 1.

Abstract

The first aim of this paper is to define the dual timelike - spacelike Mannheim partner curves in Dual Lorentzian Space ID3 1, the second aim of this paper is to obtain the relationships between the curvatures and the torsions of the dual timelike - spacelike Mannheim partner curves with respect to each other and the final aim of this paper is to get the necessary and sufficient conditions for the dual timelike -spacelike Mannheim partner curves in ID3 1 .