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: Anais da Academia Brasileira de Ciências (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=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 surfacesRibaucour transformationslinear Weingarten surfacesminimal surfacesconstant mean curvatureWe 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.Academia Brasileira de Ciências2002-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652002000400001Anais da Academia Brasileira de Ciências v.74 n.4 2002reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652002000400001info:eu-repo/semantics/openAccessTENENBLAT,KETIeng2003-01-24T00:00:00Zoai:scielo:S0001-37652002000400001Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2003-01-24T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)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
Ribaucour transformations
linear Weingarten surfaces
minimal surfaces
constant mean curvature
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 Ribaucour transformations
linear Weingarten surfaces
minimal surfaces
constant mean curvature
topic Ribaucour transformations
linear Weingarten surfaces
minimal surfaces
constant mean curvature
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 2002-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652002000400001
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652002000400001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652002000400001
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
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 Anais da Academia Brasileira de Ciências v.74 n.4 2002
reponame:Anais da Academia Brasileira de Ciências (Online)
instname:Academia Brasileira de Ciências (ABC)
instacron:ABC
instname_str Academia Brasileira de Ciências (ABC)
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institution ABC
reponame_str Anais da Academia Brasileira de Ciências (Online)
collection Anais da Academia Brasileira de Ciências (Online)
repository.name.fl_str_mv Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)
repository.mail.fl_str_mv ||aabc@abc.org.br
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