Critical principal singularities of hypersurfaces in Euclidean 4-spaces

Ronaldo Garcia, Débora Lopes, and Jorge Sotomayor

Journal of Singularities
volume 25 (2022), 150-172

Received: 28 January 2021. Received in revised form: 10 January 2022.

DOI: 10.5427/jsing.2022.25i

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Abstract:

In this work will be described the principal foliations of oriented three-dimensional manifolds immersed in Euclidean 4-spaces, near the partially umbilic set when this set is not regular. The two cases considered are generic in one parameter families of immersions and the unfolding also will be analyzed.

2010 Mathematical Subject Classification:

53A07, 53C12, 57R30, 34A09, 58K45

Key words and phrases:

Principal foliations, partially umbilic lines, critical singularities

Author(s) information:

Ronaldo Garcia
Instituto de Matemática e Estatística
Universidade Federal de Goiás
CEP 74690-900, Campus Samambaia
Goiânia, Goiás, Brazil
ragarcia@ufg.br

Débora Lopes
Departamento 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

Jorge Sotomayor
Instituto de Matemática Estatistica
Universidade de São Paulo
Rua do Matão 1010
Cidade Universitária
CEP 05508-090, São Paulo, S. P, Brazil