Generic singularities of affine distance functions and plane congruences

2025/05/24 by Igor Chagas Santos, Santos, Igor Chagas
Mathematics · #Functional Equations Stability Results #Graph theory and applications #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2505.18716

Abstract

In this paper, we classify the generic singularities of 2-parameter plane congruences in \mathbbR⁴ and the generic singularities of affine normal plane congruences. We also study the generic singularities of the family of affine distance functions.

Citations

• Binary differential equations associated to congruences of lines in Euclidean 3-space
• Singularities of Generic Line Congruences
• Equiaffine Darboux Frames for Codimension 2 Submanifolds contained in Hypersurfaces
• Equiaffine Characterization Of Lagrangian Surfaces in R⁴
• Affine metrics of locally strictly convex surfaces in affine 4-space
• Stability of C ∞ Mappings: II. Infinitesimal Stability Implies Stability

Related

• Singularities of Generic Line Congruences
• On the affine geometry of congruences of lines
• Singularities of convex hulls of smooth hypersurfaces
• Dual relations between line congruences in ℝ³ and surfaces in ℝ⁴
• Simple Cohen-Macaulay Codimension 2 Singularities