A natural Frenet frame for null curves on the lightlike cone in Minkowski space R24

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Abazari N., Bohner M., Sager I., Sedaghatdoost A., YAYLI Y.

JOURNAL OF INEQUALITIES AND APPLICATIONS, cilt.2020, sa.1, 2020 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2020 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1186/s13660-020-02500-y
  • Dergi Adı: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: Constant curvature function, Helix, Lightlike cone, Natural Frenet frame, Null curve, 51B20, 53A35, 53B30
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we investigate the representation of curves on the lightlike cone Q(2)(3) in Minkowski space R-2(4) by structure functions. In addition, with this representation, we classify all of the null curves on the lightlike cone Q(2)(3) in four types, and we obtain a natural Frenet frame for these null curves. Furthermore, for this natural Frenet frame, we calculate curvature functions of a null curve, especially the curvature function kappa(2)=0, and we show that any null curve on the lightlike cone is a helix. Finally, we find all curves with constant curvature functions.