Dual Cartan numbers and pseudo-null lines


Öztürk İ.

Mathematical Methods in the Applied Sciences, cilt.48, sa.1, ss.207-217, 2025 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1002/mma.10323
  • Dergi Adı: Mathematical Methods in the Applied Sciences
  • Derginin Tarandığı İndeksler: 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
  • Sayfa Sayıları: ss.207-217
  • Anahtar Kelimeler: Cartan frame, dual numbers, parabolic rotation, pseudo-null line
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.