Singularities of parallel surfaces

2012/03/16 by Toshizumi Fukui, Fukui, Toshizumi, Masaru Hasegawa +1 · 3 citations
Mathematics · #53A0 #58K05 #58K3 #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1203.3715

openalex publication_date 2012/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate singularities of all parallel surfaces to a given regular surface. In generic context, the types of singularities of parallel surfaces are cuspidal edge, swallowtail, cuspidal lips, cuspidal beaks, cuspidal butterfly and 3-dimensional D₄^± singularities. We give criteria for these singularities types in terms of differential geometry (Theorem 3.4 and 3.5).

Cited by

• Some counterexamples for the special lagrangian curvature equation
• Singularities of translation surfaces under the linearly dependent condition in Euclidean 3-space
• Cuspidal edges on focal surfaces of regular surfaces with parabolic points

Related

• Singularities of Maximal Surfaces
• Curvature criteria of A-simple singularities R,0-> R²,0 and their parallel curves
• Characterizing singularities of a surface in Lie sphere geometry
• Cuspidal edges on focal surfaces of regular surfaces with parabolic points
• On the geometry of folded cuspidal edges