New results concerning Cartan null and pseudo null curves in Minkowski 3-space

CAMCI Ç., Uçum A., İlarslan K.

Journal of Geometry, vol.114, no.2, 2023 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 114 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1007/s00022-023-00676-4
  • Journal Name: Journal of Geometry
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Keywords: Flat surface, Minimal surface, Minkowski 3-space, Null curves, Parallel Frenet frames, Pseudo null curves
  • Çanakkale Onsekiz Mart University Affiliated: Yes

Abstract

In this study, we focus on Cartan null and pseudo null curves in Minkowski 3-space E13 . Firstly we define Cartan null and pseudo null equivalent curves and give the related examples. Then we give a construction method for Cartan null curves and it is shown that every Cartan null curve can be obtained from a timelike curve lying in the Lorentz plane in E13 . Also a construction method is given for pseudo null curves and we show that all pseudo null curves lie in a lightlike plane in E13 . Finally we define a new surface in E13 called “surface of pseudo null curves” and we obtain the geometric properties of such surfaces.