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Mannheim curves and their partner curves in Minkowski 3-space E13

Elsharkawy Ayman, Elshenhab Ahmed M.

Demonstratio Mathematica

2022

Vol. 55, nr 1

798--811

The modified orthogonal frame is an important tool to study analytic space curves whose curvatures have discrete zero points. In this article, by using the modified orthogonal frame, Mannheim curves and their partner curves are investigated in Minkowski 3-space. Some characterizations according to the curvatures and torsions of the curves are given. Finally, some relations under the conditions for Mannheim curves and their partner curves to be generalized helices are presented. All the possible cases for the partner curves to be spacelike and timelike are considered in the whole of the article.

On the Dual Darboux rotation axis of the spacelike Dual space curve

Ayyildiz N., Çöken A. C., Yücesan A.

Demonstratio Mathematica

2004

Vol. 37, nr 1

197--202

In this paper, the Dual Darboux rotation axis for spacelike dual space curve in the semi-dual space D3 is decomposed in two simultaneous rotations. The axis of these simultaneous rotations are joined by a simple mechanism. This study is original corresponding in the semi-dual space D3 of the article entitled On the Dual Darboux Rotation Axis of the Dual Space Curve [6].