Isometric deformation of surfaces in R 3 preserving the mean curvature function

Detalhes bibliográficos
Autor(a) principal: Colares, Antonio Gervásio
Data de Publicação: 1989
Outros Autores: Kenmotsu, Katsuei
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
Texto Completo: http://www.repositorio.ufc.br/handle/riufc/40845
Resumo: The purpose of this paper is to classify surfaces in Euclidean 3- space with constant Gaussian curvature which admit non-trivial oneparameter families of isometric immersions preserving the mean curvature function. It is shown that the Gaussian curvature must be zero and, if the mean curvature is not constant, then such isometric immersions are some deformations of the cylinder over a logarithmic spiral.
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spelling Isometric deformation of surfaces in R 3 preserving the mean curvature functionEspaço euclidianoImersões (Matemática)Curvatura médiaThe purpose of this paper is to classify surfaces in Euclidean 3- space with constant Gaussian curvature which admit non-trivial oneparameter families of isometric immersions preserving the mean curvature function. It is shown that the Gaussian curvature must be zero and, if the mean curvature is not constant, then such isometric immersions are some deformations of the cylinder over a logarithmic spiral.Pacific Journal of Mathematics2019-04-12T13:40:34Z2019-04-12T13:40:34Z1989info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfCOLARES, Antônio Gervásio; KENMOTSU,Katsuei. Isometric deformation of surfaces in R 3 preserving the mean curvature function. Pacific Journal of Mathematics, USA, v. 136, n.1, p. 71-80, 1989.http://www.repositorio.ufc.br/handle/riufc/40845Colares, Antonio GervásioKenmotsu, Katsueiinfo:eu-repo/semantics/openAccessengreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFC2023-10-31T14:37:24Zoai:repositorio.ufc.br:riufc/40845Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2023-10-31T14:37:24Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false
dc.title.none.fl_str_mv Isometric deformation of surfaces in R 3 preserving the mean curvature function
title Isometric deformation of surfaces in R 3 preserving the mean curvature function
spellingShingle Isometric deformation of surfaces in R 3 preserving the mean curvature function
Colares, Antonio Gervásio
Espaço euclidiano
Imersões (Matemática)
Curvatura média
title_short Isometric deformation of surfaces in R 3 preserving the mean curvature function
title_full Isometric deformation of surfaces in R 3 preserving the mean curvature function
title_fullStr Isometric deformation of surfaces in R 3 preserving the mean curvature function
title_full_unstemmed Isometric deformation of surfaces in R 3 preserving the mean curvature function
title_sort Isometric deformation of surfaces in R 3 preserving the mean curvature function
author Colares, Antonio Gervásio
author_facet Colares, Antonio Gervásio
Kenmotsu, Katsuei
author_role author
author2 Kenmotsu, Katsuei
author2_role author
dc.contributor.author.fl_str_mv Colares, Antonio Gervásio
Kenmotsu, Katsuei
dc.subject.por.fl_str_mv Espaço euclidiano
Imersões (Matemática)
Curvatura média
topic Espaço euclidiano
Imersões (Matemática)
Curvatura média
description The purpose of this paper is to classify surfaces in Euclidean 3- space with constant Gaussian curvature which admit non-trivial oneparameter families of isometric immersions preserving the mean curvature function. It is shown that the Gaussian curvature must be zero and, if the mean curvature is not constant, then such isometric immersions are some deformations of the cylinder over a logarithmic spiral.
publishDate 1989
dc.date.none.fl_str_mv 1989
2019-04-12T13:40:34Z
2019-04-12T13:40:34Z
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 COLARES, Antônio Gervásio; KENMOTSU,Katsuei. Isometric deformation of surfaces in R 3 preserving the mean curvature function. Pacific Journal of Mathematics, USA, v. 136, n.1, p. 71-80, 1989.
http://www.repositorio.ufc.br/handle/riufc/40845
identifier_str_mv COLARES, Antônio Gervásio; KENMOTSU,Katsuei. Isometric deformation of surfaces in R 3 preserving the mean curvature function. Pacific Journal of Mathematics, USA, v. 136, n.1, p. 71-80, 1989.
url http://www.repositorio.ufc.br/handle/riufc/40845
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 Pacific Journal of Mathematics
publisher.none.fl_str_mv Pacific Journal of Mathematics
dc.source.none.fl_str_mv reponame:Repositório Institucional da Universidade Federal do Ceará (UFC)
instname:Universidade Federal do Ceará (UFC)
instacron:UFC
instname_str Universidade Federal do Ceará (UFC)
instacron_str UFC
institution UFC
reponame_str Repositório Institucional da Universidade Federal do Ceará (UFC)
collection Repositório Institucional da Universidade Federal do Ceará (UFC)
repository.name.fl_str_mv Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)
repository.mail.fl_str_mv bu@ufc.br || repositorio@ufc.br
_version_ 1809935777956626432

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