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Singularities of 3-parameter line congruences in $\mathbb {R}^{4}$

Published online by Cambridge University Press:  21 June 2022

Débora Lopes
Affiliation:
Departmento de Matemática, Universidade Federal do Sergipe Av. Marechal Rondon, s/n Jardim Rosa Elze - CEP 49100-000 São Cristóvão, SE, Brazil (deb@deboralopes.mat.br)
Maria Aparecida Soares Ruas
Affiliation:
Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Av. Trabalhador S ao-carlense 400, São Carlos, SP 13566-590, Brazil (maasruas@icmc.usp.br, igor.chs34@usp.br)
Igor Chagas Santos
Affiliation:
Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Av. Trabalhador S ao-carlense 400, São Carlos, SP 13566-590, Brazil (maasruas@icmc.usp.br, igor.chs34@usp.br)

Abstract

In this paper, we give the generic classification of the singularities of 3-parameter line congruences in $\mathbb {R}^{4}$. We also classify the generic singularities of normal and Blaschke (affine) normal congruences.

Type
Research Article
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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