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

Creative Commons License

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

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

  • 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
  • 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.