On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces

Detalhes bibliográficos
Autor(a) principal: Colares, Antônio Gervásio
Data de Publicação: 2011
Outros Autores: Velasco, Oscar Alfredo Palmas
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
dARK ID: ark:/83112/0013000003rpc
Texto Completo: http://www.repositorio.ufc.br/handle/riufc/4403
Resumo: In this paper we define closed partially conformal vector fields and use them to give a characterization of Riemannian manifolds which admit this kind of fields as some special warped products foliated by (n − 1)-umbilical hypersurfaces. Examples are described in space forms. In particular, closed partially conformal vector fields in Euclidean spaces are associated to the most simple foliations given by hyperspheres, hyperplanes or coaxial cylinders. Finally, for manifolds admitting such vector fields, we impose conditions for a hypersurface to be (n − 1)-umbilical, or, in particular, a leaf of the corresponding foliation.
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spelling On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfacesCurvaturaHipersuperfíciesVariedades riemanianasIn this paper we define closed partially conformal vector fields and use them to give a characterization of Riemannian manifolds which admit this kind of fields as some special warped products foliated by (n − 1)-umbilical hypersurfaces. Examples are described in space forms. In particular, closed partially conformal vector fields in Euclidean spaces are associated to the most simple foliations given by hyperspheres, hyperplanes or coaxial cylinders. Finally, for manifolds admitting such vector fields, we impose conditions for a hypersurface to be (n − 1)-umbilical, or, in particular, a leaf of the corresponding foliation.2013-02-05T13:43:52Z2013-02-05T13:43:52Z2011info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfCOLARES, Antônio Gervásio ; PALMAS VELASCO, Oscar Alfredo. On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces. Bulletin Brazilian Mathematical Society, v. 42, n. 1, p. 105-130, 2011.http://www.repositorio.ufc.br/handle/riufc/4403ark:/83112/0013000003rpcColares, Antônio GervásioVelasco, Oscar Alfredo Palmasinfo:eu-repo/semantics/openAccessengreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFC2023-10-31T14:37:40Zoai:repositorio.ufc.br:riufc/4403Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2024-09-11T18:30:55.386692Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false
dc.title.none.fl_str_mv On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces
title On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces
spellingShingle On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces
Colares, Antônio Gervásio
Curvatura
Hipersuperfícies
Variedades riemanianas
title_short On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces
title_full On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces
title_fullStr On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces
title_full_unstemmed On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces
title_sort On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces
author Colares, Antônio Gervásio
author_facet Colares, Antônio Gervásio
Velasco, Oscar Alfredo Palmas
author_role author
author2 Velasco, Oscar Alfredo Palmas
author2_role author
dc.contributor.author.fl_str_mv Colares, Antônio Gervásio
Velasco, Oscar Alfredo Palmas
dc.subject.por.fl_str_mv Curvatura
Hipersuperfícies
Variedades riemanianas
topic Curvatura
Hipersuperfícies
Variedades riemanianas
description In this paper we define closed partially conformal vector fields and use them to give a characterization of Riemannian manifolds which admit this kind of fields as some special warped products foliated by (n − 1)-umbilical hypersurfaces. Examples are described in space forms. In particular, closed partially conformal vector fields in Euclidean spaces are associated to the most simple foliations given by hyperspheres, hyperplanes or coaxial cylinders. Finally, for manifolds admitting such vector fields, we impose conditions for a hypersurface to be (n − 1)-umbilical, or, in particular, a leaf of the corresponding foliation.
publishDate 2011
dc.date.none.fl_str_mv 2011
2013-02-05T13:43:52Z
2013-02-05T13:43:52Z
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 ; PALMAS VELASCO, Oscar Alfredo. On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces. Bulletin Brazilian Mathematical Society, v. 42, n. 1, p. 105-130, 2011.
http://www.repositorio.ufc.br/handle/riufc/4403
dc.identifier.dark.fl_str_mv ark:/83112/0013000003rpc
identifier_str_mv COLARES, Antônio Gervásio ; PALMAS VELASCO, Oscar Alfredo. On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces. Bulletin Brazilian Mathematical Society, v. 42, n. 1, p. 105-130, 2011.
ark:/83112/0013000003rpc
url http://www.repositorio.ufc.br/handle/riufc/4403
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.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
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