On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces
Autor(a) principal: | |
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Data de Publicação: | 2011 |
Outros Autores: | |
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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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 |
_version_ |
1818373701159092224 |