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arXiv · 2210.14175

Line Congruences on singular surfaces

Débora Lopes·Tito Alexandro Medina Tejeda·Maria Aparecida Soares Ruas·Igor Chagas Santos
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Abstract

This paper is a first step in order to extend Kummer's theory for line congruences to the case $\lbrace x, \xi \rbrace $, where $x: U \rightarrow \mathbb{R}^3$ is a smooth map and $\xi: U \rightarrow \mathbb{R}^3$ is a proper frontal. We show that if $\lbrace x, \xi \rbrace$ 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 $\xi$.

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Débora Lopes, Tito Alexandro Medina Tejeda, Maria Aparecida Soares Ruas, Igor Chagas Santos. 2022-10-25. Line Congruences on singular surfaces. https://arxiv.org/abs/2210.14175

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