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- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021
- ISSN
- 0188-7009
- eISSN
- 1661-4909
- DOI
- 10.1007/s00006-021-01176-x
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we define and classify split quaternion operators. Then, we show that the split quaternion product of a split quaternion operator and a curve, which lies on Lorentzian unit sphere or on hyperbolic unit sphere, parametrizes a ruled surface in the 3-dimensional Minkowski space E13\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb {E}_{1}^{3}$$\end{document} if the vector part of the operator is perpendicular to the position vector of the spherical curve. Moreover, the ruled surfaces are represented as 2-parameter homothetic motions in E13\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb {E}_{1}^{3}$$\end{document} by using semi-orthogonal matrices corresponding to the split quaternion operators. Finally, some examples are given to illustrate some applications of our main results.
Journal
Advances in Applied Clifford Algebras – Springer Journals
Published: Nov 1, 2021
Keywords: Split quaternions; Ruled surfaces; Minkowski 3-space; Spherical curves in Minkowski 3-space; 2-parameter homothetic motions; 14J26; 70E15; 70E18; 11R52; 37E45; 51B20; 53A35; 70B10