Legendrian dual surfaces of a spacelike curve in the 3-dimensional lightcone

Saji K., Yıldırım H.

JOURNAL OF GEOMETRY AND PHYSICS, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.geomphys.2022.104593
  • Dergi Adı: JOURNAL OF GEOMETRY AND PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: 3-dimensional lightcone, Legendrian dual surfaces, Legendrian dualities, Singularities, Spacelike curve
  • İstanbul Üniversitesi Adresli: Evet

Özet

In this paper, we study Legendrian dual surfaces, lying in the 3-dimensional pseudo(hyper)spheres of various radii in Lorentz-Minkowski 4-space, of a spacelike curve in the 3-dimensional lightcone. We point out that these surfaces are constructed by the extended Legendrian dualities between the 3-dimensional lightcone and these 3dimensional pseudo-spheres. Moreover, we investigate the singularities of these surfaces and show the dualities of the singularities of a certain class of such a surface in the 3dimensional lightcone. Furthermore, we deal with the singularities of all of these surfaces when they are non-flat.