Line Congruences on singular surfaces

2022/10/25 by Débora Lopes, Tito Alexandro Medina Tejeda, Lopes, Débora +5
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2210.14175

openalex publication_date 2022/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is a first step in order to extend Kummer's theory for line congruences to the case \lbrace x, ξ\rbrace , where x: U → ℝ³ is a smooth map and ξ: U → ℝ³ is a proper frontal. We show that if \lbrace x, ξ\rbrace is a normal congruence, the equation of the principal surfaces is a multiple of the equation of the developable surfaces, furthermore, the multiplicative factor is associated to the singular set of ξ.

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