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

Part of: Classical differential geometry Theory of singularities and catastrophe theory Differential topology

Published online by Cambridge University Press:  21 June 2022

Débora Lopes Open the ORCID record for Débora Lopes [Opens in a new window] ,
Maria Aparecida Soares Ruas Open the ORCID record for Maria Aparecida Soares Ruas [Opens in a new window]  and
Igor Chagas Santos Open the ORCID record for Igor Chagas Santos [Opens in a new window]
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)
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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.

Keywords

Line congruencesBlaschke normal congruencesLagrangian singularities

MSC classification

Primary: 57R45: Singularities of differentiable mappings
Secondary: 58K25: Stability 53A15: Affine differential geometry
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 3 , June 2023 , pp. 1045 - 1070
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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