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

Shyuichi Izumiya, Ana Claudia Nabarro, and Andrea de Jesus Sacramento

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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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.

Author(s) information:

Shyuichi Izumiya Ana Claudia Nabarro Andrea de Jesus Sacramento
Department of Mathematics Departamento de Matemática Departamento de Matemática
Hokkaido University ICMC Universidade de São Paulo ICMC Universidade de São Paulo
Sapporo 060-0810, Japan Campus de São Carlos Campus de São Carlos
Caixa Postal 668 Caixa Postal 668
CEP 13560-970, São Carlos-SP, Brazil CEP 13560-970, São Carlos-SP, Brazil
email: izumiya@math.sci.hokudai.ac.jp email: anaclana@icmc.usp.br email: anddyunesp@yahoo.com.br