Horospherical and hyperbolic dual surfaces of spacelike curves in de Sitter space

Journal of Singularities
volume 16 (2017), 180-193

Received: 2 August 2016. Received in revised form: 29 June 2017.

DOI: 10.5427/jsing.2017.16h

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Abstract:

We define two surfaces, the horospherical surface and the hyperbolic dual surface of a spacelike curve in the de Sitter 3-space, in the Lorentzian-Minkowski 4-space. These surfaces are, respectively, in the lightcone 3-space and in the hyperbolic 3-space (other pseudo-spheres). We use techniques from singularity theory to obtain the generic shape of these surfaces and of their singular point sets. Furthermore, we give a relation between these surfaces from the viewpoint of the theory of Legendrian dualities between pseudo-spheres.