Legendrian dual surfaces of a spacelike curve in the 3-dimensional lightcone
JOURNAL OF GEOMETRY AND PHYSICS, 2022 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Publication Date: 2022
- Doi Number: 10.1016/j.geomphys.2022.104593
- Journal Name: JOURNAL OF GEOMETRY AND PHYSICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
- Keywords: 3-dimensional lightcone, Legendrian dual surfaces, Legendrian dualities, Singularities, Spacelike curve
- Istanbul University Affiliated: Yes
Abstract
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.