Lightcone dualities for curves in the lightcone unit 3-sphere

Abstract

In this paper, we consider the curves in the unit 3-sphere in the lightcone. The unit 3-sphere can be canonically embedded in the lightcone and de Sitter 4-space in Lorentz-Minkowski 5-space. We investigate these curves in the framework of the theory of Legendrian dualities between pseudo-spheres in Lorentz-Minkowski 5-space.