2022/11/01 by Anderson Reis de Vargas, de Vargas, Anderson Reis, Marcos Craizer +1
Computer Science · Engineering · #53A15 #53A70 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #Digital Image Processing Techniques #FOS: Mathematics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2211.00442
openalex publication_date 2022/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider in this paper 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 a quite difficult task, and our results can be considered as a fisrt step in this direction. We also prove some characterizations of ruled discrete improper affine spheres which are analogous to the smooth case.