Dual Cartan numbers and pseudo-null lines
Mathematical Methods in the Applied Sciences, vol.48, no.1, pp.207-217, 2025 (SCI-Expanded)
- Publication Type: Article / Article
- Volume: 48 Issue: 1
- Publication Date: 2025
- Doi Number: 10.1002/mma.10323
- Journal Name: Mathematical Methods in the Applied Sciences
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
- Page Numbers: pp.207-217
- Keywords: Cartan frame, dual numbers, parabolic rotation, pseudo-null line
- Akdeniz University Affiliated: Yes
Abstract
The study aims to introduce some geometric properties of dual Cartan numbers. Since a unit timelike Cartan number with lightlike vector part corresponds to a parabolic rotation around a lightlike axis, it has been shown that the unit dual Cartan number with lightlike dual vector also corresponds to a parabolic rotation and a translation transformation in the Cartan frame. Also, the angle between the directed pseudo-null lines that tangent the same parabola is defined. Thus, the rotation and translation relationship between two directed pseudo-null lines is obtained. Also, the E. Study transformation is given for the directed pseudo-null lines.