On the index of principal foliations of surfaces in R3with corank 1 singularities

Detalhes bibliográficos
Autor(a) principal: Costa, J. C.F. [UNESP]
Data de Publicação: 2020
Outros Autores: Martins, L. F. [UNESP], Nuńo-Ballesteros, J. J.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.5427/jsing.2020.22a
http://hdl.handle.net/11449/205381
Resumo: It is well known that the index associated to the principal foliations at a cross-cap point is 1/2. In this work we study the index for other corank 1 singularities from (R2, 0) to (R3, 0) which either are simple or are non-simple but included in strata of Ae-codimension ≤ 3. We show that the index, under certain conditions, is always 0 or 1, bearing out that the Loewner conjecture could be true for all corank 1 singularities.
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spelling On the index of principal foliations of surfaces in R3with corank 1 singularitiesIndexLowener conjecturePrincipal linesSingular surfacesIt is well known that the index associated to the principal foliations at a cross-cap point is 1/2. In this work we study the index for other corank 1 singularities from (R2, 0) to (R3, 0) which either are simple or are non-simple but included in strata of Ae-codimension ≤ 3. We show that the index, under certain conditions, is always 0 or 1, bearing out that the Loewner conjecture could be true for all corank 1 singularities.Departamento de Matemática UNESP - Universidade Estadual Paulista, R. Cristóvão Colombo, 2265Departament de Geometria i Topologia Universitat de València, Campus de BurjassotDepartamento de Matemática UNESP - Universidade Estadual Paulista, R. Cristóvão Colombo, 2265Universidade Estadual Paulista (Unesp)Universitat de ValènciaCosta, J. C.F. [UNESP]Martins, L. F. [UNESP]Nuńo-Ballesteros, J. J.2021-06-25T10:14:22Z2021-06-25T10:14:22Z2020-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1-16http://dx.doi.org/10.5427/jsing.2020.22aJournal of Singularities, v. 22, p. 1-16.1949-2006http://hdl.handle.net/11449/20538110.5427/jsing.2020.22a2-s2.0-85094116621Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Singularitiesinfo:eu-repo/semantics/openAccess2021-10-23T12:39:59Zoai:repositorio.unesp.br:11449/205381Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:23:33.917436Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv On the index of principal foliations of surfaces in R3with corank 1 singularities
title On the index of principal foliations of surfaces in R3with corank 1 singularities
spellingShingle On the index of principal foliations of surfaces in R3with corank 1 singularities
Costa, J. C.F. [UNESP]
Index
Lowener conjecture
Principal lines
Singular surfaces
title_short On the index of principal foliations of surfaces in R3with corank 1 singularities
title_full On the index of principal foliations of surfaces in R3with corank 1 singularities
title_fullStr On the index of principal foliations of surfaces in R3with corank 1 singularities
title_full_unstemmed On the index of principal foliations of surfaces in R3with corank 1 singularities
title_sort On the index of principal foliations of surfaces in R3with corank 1 singularities
author Costa, J. C.F. [UNESP]
author_facet Costa, J. C.F. [UNESP]
Martins, L. F. [UNESP]
Nuńo-Ballesteros, J. J.
author_role author
author2 Martins, L. F. [UNESP]
Nuńo-Ballesteros, J. J.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Universitat de València
dc.contributor.author.fl_str_mv Costa, J. C.F. [UNESP]
Martins, L. F. [UNESP]
Nuńo-Ballesteros, J. J.
dc.subject.por.fl_str_mv Index
Lowener conjecture
Principal lines
Singular surfaces
topic Index
Lowener conjecture
Principal lines
Singular surfaces
description It is well known that the index associated to the principal foliations at a cross-cap point is 1/2. In this work we study the index for other corank 1 singularities from (R2, 0) to (R3, 0) which either are simple or are non-simple but included in strata of Ae-codimension ≤ 3. We show that the index, under certain conditions, is always 0 or 1, bearing out that the Loewner conjecture could be true for all corank 1 singularities.
publishDate 2020
dc.date.none.fl_str_mv 2020-01-01
2021-06-25T10:14:22Z
2021-06-25T10:14:22Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.5427/jsing.2020.22a
Journal of Singularities, v. 22, p. 1-16.
1949-2006
http://hdl.handle.net/11449/205381
10.5427/jsing.2020.22a
2-s2.0-85094116621
url http://dx.doi.org/10.5427/jsing.2020.22a
http://hdl.handle.net/11449/205381
identifier_str_mv Journal of Singularities, v. 22, p. 1-16.
1949-2006
10.5427/jsing.2020.22a
2-s2.0-85094116621
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Singularities
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 1-16
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
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