| Texto completo | |
| Autor(es): |
da Silva, Debora Lopes
;
Tejeda, Tito Alexandro Medina
;
Ruas, Maria Aparecida Soares
;
Santos, Igor Chagas
Número total de Autores: 4
|
| Tipo de documento: | Artigo Científico |
| Fonte: | BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 56, n. 4, p. 22-pg., 2025-11-19. |
| Resumo | |
In this paper, we extend Kummer's theory for line congruences to the case {x,xi}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lbrace x, \xi \rbrace $$\end{document}, where x:U -> R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x: U \rightarrow \mathbb {R}<^>3$$\end{document} is a smooth map and xi:U -> R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\xi : U \rightarrow \mathbb {R}<^>3$$\end{document} is a proper frontal. We show that if {x,xi}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lbrace x, \xi \rbrace $$\end{document} is a normal congruence, the equation of the principal surfaces is a multiple of the equation of the developable surfaces, furthermore, the zero set of this multiplicative factor is the singular set of xi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\xi $$\end{document}. (AU) | |
| Processo FAPESP: | 19/21181-0 - Novas fronteiras na Teoria de Singularidades |
| Beneficiário: | Regilene Delazari dos Santos Oliveira |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 21/11253-3 - Geometria dos frontais em codimensão arbitrária |
| Beneficiário: | Tito Alexandro Medina Tejeda |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |