Some Characterizations for a Quaternion-Valued and Dual Variable Curve

Author:

Karadag Muge,Sivridag Ali

Abstract

Quaternions, which are found in many fields, have been studied for a long time. The interest in dual quaternions has also increased after real quaternions. Nagaraj and Bharathi developed the basic theories of these studies. The Serret–Frenet Formulae for dual quaternion-valued functions of one real variable are derived. In this paper, by making use of the results of some previous studies, helixes and harmonic curvature concepts in Q D 3 and Q D 4 are considered and a characterization for a dual harmonic curve to be a helix is given.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Reference5 articles.

1. Geometry of Quaternionic and Pseudo-Quaternionic Multiplications;Bharathi;Ind. J. Pure Appl. Math.,1985

2. Quaternion Valued Function of a Real Variable Serret-Frenet Formulae;Bharathi;Ind. J. Pure Appl. Math.,1987

3. Motion Geometry and Quaternions Theory;Hacisalihoğlu,1983

4. The Serret-Frenet formulae for dual quaternion-valued functions of a single real variable

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Winding number and homotopy for quaternionic curves;International Journal of Geometric Methods in Modern Physics;2022-03-15

2. A primer on the differential geometry of quaternionic curves;Mathematical Methods in the Applied Sciences;2021-08-05

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