Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi-Calò method

Detalhes bibliográficos
Autor(a) principal: LIMA,LEVI L. DE
Data de Publicação: 2002
Outros Autores: ROITMAN,PEDRO
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=S0001-37652002000100002
Resumo: In this note we present a method for constructing constant mean curvature on surfaces in hyperbolic 3-space in terms of holomorphic data first introduced in Bianchi's Lezioni di Geometria Differenziale of 1927, therefore predating by many years the modern approaches due to Bryant, Small and others. Besides its obvious historical interest, this note aims to complement Bianchi's analysis by deriving explicit formulae for CMC-1 surfaces and comparing the various approaches encountered in the literature.
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spelling Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi-Calò methodConstant mean curvature one surfacescongruence of spheresrolling of surfacesWeierstrass representationIn this note we present a method for constructing constant mean curvature on surfaces in hyperbolic 3-space in terms of holomorphic data first introduced in Bianchi's Lezioni di Geometria Differenziale of 1927, therefore predating by many years the modern approaches due to Bryant, Small and others. Besides its obvious historical interest, this note aims to complement Bianchi's analysis by deriving explicit formulae for CMC-1 surfaces and comparing the various approaches encountered in the literature.Academia Brasileira de Ciências2002-03-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652002000100002Anais da Academia Brasileira de Ciências v.74 n.1 2002reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652002000100002info:eu-repo/semantics/openAccessLIMA,LEVI L. DEROITMAN,PEDROeng2002-05-24T00:00:00Zoai:scielo:S0001-37652002000100002Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2002-05-24T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi-Calò method
title Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi-Calò method
spellingShingle Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi-Calò method
LIMA,LEVI L. DE
Constant mean curvature one surfaces
congruence of spheres
rolling of surfaces
Weierstrass representation
title_short Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi-Calò method
title_full Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi-Calò method
title_fullStr Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi-Calò method
title_full_unstemmed Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi-Calò method
title_sort Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi-Calò method
author LIMA,LEVI L. DE
author_facet LIMA,LEVI L. DE
ROITMAN,PEDRO
author_role author
author2 ROITMAN,PEDRO
author2_role author
dc.contributor.author.fl_str_mv LIMA,LEVI L. DE
ROITMAN,PEDRO
dc.subject.por.fl_str_mv Constant mean curvature one surfaces
congruence of spheres
rolling of surfaces
Weierstrass representation
topic Constant mean curvature one surfaces
congruence of spheres
rolling of surfaces
Weierstrass representation
description In this note we present a method for constructing constant mean curvature on surfaces in hyperbolic 3-space in terms of holomorphic data first introduced in Bianchi's Lezioni di Geometria Differenziale of 1927, therefore predating by many years the modern approaches due to Bryant, Small and others. Besides its obvious historical interest, this note aims to complement Bianchi's analysis by deriving explicit formulae for CMC-1 surfaces and comparing the various approaches encountered in the literature.
publishDate 2002
dc.date.none.fl_str_mv 2002-03-01
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=S0001-37652002000100002
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652002000100002
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652002000100002
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.1 2002
reponame:Anais da Academia Brasileira de Ciências (Online)
instname:Academia Brasileira de Ciências (ABC)
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instname_str Academia Brasileira de Ciências (ABC)
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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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