Singularities of discrete improper indefinite affine spheres

Singularities of discrete improper indefinite affine spheres

In this paper we consider discrete improper affine spheres based on asymptotic nets. In this context, we distinguish the discrete edges and vertices that must be considered singular. The singular edges can be considered as discrete cuspidal edges, while some of the singular vertices can be considere...

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Veröffentlicht in:Journal of geometry 2023-12, Vol.114 (3), Article 34
Hauptverfasser: de Vargas, Anderson Reis, Craizer, Marcos
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Geometry
Graph theory
Mathematics
Mathematics and Statistics
Singularities
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description In this paper we consider discrete improper affine spheres based on asymptotic nets. In this context, we distinguish the discrete edges and vertices that must be considered singular. The singular edges can be considered as discrete cuspidal edges, while some of the singular vertices can be considered as discrete swallowtails. The classification of singularities of discrete nets is quite a difficult task, and our results can be seen as a first step in this direction. We also prove some characterizations of ruled discrete improper affine spheres which are analogous to the smooth case.
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subjects Apexes
Geometry
Graph theory
Mathematics
Mathematics and Statistics
Singularities
title Singularities of discrete improper indefinite affine spheres
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