On Ribaucour transformations and applications to linear Weingarten surfaces

Detalhes bibliográficos
Autor(a) principal: TENENBLAT, KETI
Data de Publicação: 2002
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UnB
Texto Completo: http://repositorio.unb.br/handle/10482/25822
https://dx.doi.org/10.1590/S0001-37652002000400001
Resumo: We present a revised definition of a Ribaucour transformation for submanifolds of space forms, with flat normal bundle, motivated by the classical definition and by more recent extensions. The new definition provides a precise treatment of the geometric aspect of such transformations preserving lines of curvature and it can be applied to submanifolds whose principal curvatures have multiplicity bigger than one. Ribaucour transformations are applied as a method of obtaining linear Weingarten surfaces contained in Euclidean space, from a given such surface. Examples are included for minimal surfaces, constant mean curvature and linear Weingarten surfaces. The examples show the existence of complete hyperbolic linear Weingarten surfaces in Euclidean space.
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spelling On Ribaucour transformations and applications to linear Weingarten surfacesTransformações de RibaucourSuperfícies de WeingartenSuperfícies mínimasCurvatura média constanteWe present a revised definition of a Ribaucour transformation for submanifolds of space forms, with flat normal bundle, motivated by the classical definition and by more recent extensions. The new definition provides a precise treatment of the geometric aspect of such transformations preserving lines of curvature and it can be applied to submanifolds whose principal curvatures have multiplicity bigger than one. Ribaucour transformations are applied as a method of obtaining linear Weingarten surfaces contained in Euclidean space, from a given such surface. Examples are included for minimal surfaces, constant mean curvature and linear Weingarten surfaces. The examples show the existence of complete hyperbolic linear Weingarten surfaces in Euclidean space.Apresentamos uma definição de tranformação de Ribaucour revisada, para subvariedades de formas espaciais com fibrado normal plano, motivados pela definição clássica e pelas extensões mais recentes. A nova definição fornece um tratamento preciso do aspecto geométrico de tais transformações preservarem linhas de curvatura e pode ser aplicada a subvariedades cujas curvaturas principais têm multiplicidade maior que um. Transformações de Ribaucour são aplicadas como um método para obtenção de superfícies de Weingarten lineares, contidas no espaço Euclideano, a partir de uma dada superfície deste tipo. Exemplos são incluidos para superfícies mínimas, superfícies de curvatura média constante e superfícies linear Weingarten. Os exemplos mostram a existência de superfícies linear Weingarten, hiperbólicas, completas no espaço Euclideano.Em processamentoAcademia Brasileira de Ciências2017-12-07T04:35:25Z2017-12-07T04:35:25Z2002info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfAn. Acad. Bras. Ciênc.,v.74,n.4,p.559-575,2002http://repositorio.unb.br/handle/10482/25822https://dx.doi.org/10.1590/S0001-37652002000400001TENENBLAT, KETIinfo:eu-repo/semantics/openAccessengreponame:Repositório Institucional da UnBinstname:Universidade de Brasília (UnB)instacron:UNB2024-08-28T16:27:55Zoai:repositorio.unb.br:10482/25822Repositório InstitucionalPUBhttps://repositorio.unb.br/oai/requestrepositorio@unb.bropendoar:2024-08-28T16:27:55Repositório Institucional da UnB - Universidade de Brasília (UnB)false
dc.title.none.fl_str_mv On Ribaucour transformations and applications to linear Weingarten surfaces
title On Ribaucour transformations and applications to linear Weingarten surfaces
spellingShingle On Ribaucour transformations and applications to linear Weingarten surfaces
TENENBLAT, KETI
Transformações de Ribaucour
Superfícies de Weingarten
Superfícies mínimas
Curvatura média constante
title_short On Ribaucour transformations and applications to linear Weingarten surfaces
title_full On Ribaucour transformations and applications to linear Weingarten surfaces
title_fullStr On Ribaucour transformations and applications to linear Weingarten surfaces
title_full_unstemmed On Ribaucour transformations and applications to linear Weingarten surfaces
title_sort On Ribaucour transformations and applications to linear Weingarten surfaces
author TENENBLAT, KETI
author_facet TENENBLAT, KETI
author_role author
dc.contributor.author.fl_str_mv TENENBLAT, KETI
dc.subject.por.fl_str_mv Transformações de Ribaucour
Superfícies de Weingarten
Superfícies mínimas
Curvatura média constante
topic Transformações de Ribaucour
Superfícies de Weingarten
Superfícies mínimas
Curvatura média constante
description We present a revised definition of a Ribaucour transformation for submanifolds of space forms, with flat normal bundle, motivated by the classical definition and by more recent extensions. The new definition provides a precise treatment of the geometric aspect of such transformations preserving lines of curvature and it can be applied to submanifolds whose principal curvatures have multiplicity bigger than one. Ribaucour transformations are applied as a method of obtaining linear Weingarten surfaces contained in Euclidean space, from a given such surface. Examples are included for minimal surfaces, constant mean curvature and linear Weingarten surfaces. The examples show the existence of complete hyperbolic linear Weingarten surfaces in Euclidean space.
publishDate 2002
dc.date.none.fl_str_mv 2002
2017-12-07T04:35:25Z
2017-12-07T04:35:25Z
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 An. Acad. Bras. Ciênc.,v.74,n.4,p.559-575,2002
http://repositorio.unb.br/handle/10482/25822
https://dx.doi.org/10.1590/S0001-37652002000400001
identifier_str_mv An. Acad. Bras. Ciênc.,v.74,n.4,p.559-575,2002
url http://repositorio.unb.br/handle/10482/25822
https://dx.doi.org/10.1590/S0001-37652002000400001
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Academia Brasileira de Ciências
publisher.none.fl_str_mv Academia Brasileira de Ciências
dc.source.none.fl_str_mv reponame:Repositório Institucional da UnB
instname:Universidade de Brasília (UnB)
instacron:UNB
instname_str Universidade de Brasília (UnB)
instacron_str UNB
institution UNB
reponame_str Repositório Institucional da UnB
collection Repositório Institucional da UnB
repository.name.fl_str_mv Repositório Institucional da UnB - Universidade de Brasília (UnB)
repository.mail.fl_str_mv repositorio@unb.br
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