Integral formulae for spacelikehypersurfaces in conformally stationary spacetimes and applications

Bibliographic Details
Main Author: Alías, Luís J.
Publication Date: 2003
Other Authors: Brasil Júnior, Aldir Chaves, Colares, Antônio Gervásio
Format: Article
Language: eng
Source: Repositório Institucional da Universidade Federal do Ceará (UFC)
Download full: http://www.repositorio.ufc.br/handle/riufc/4631
Summary: In this paper we develop general Minkowski-type formulae for compact spacelike hypersurfaces immersed into conformally stationary spacetimes, that is, Lorentzian manifolds admitting a timelike conformal field. We apply them to the study of the umbilicity of compact spacelike hypersurfaces in terms of their r-mean curvatures. We derive several uniqueness results, for instance, compact spacelike hypersurfaces are umbilical if either some of their r-mean curvatures are linearly related or one of them is constant.
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spelling Alías, Luís J.Brasil Júnior, Aldir ChavesColares, Antônio Gervásio2013-02-28T13:25:28Z2013-02-28T13:25:28Z2003ALIÁS, Luis J. ; BRASIL JÚNIOR, Aldir Chaves ; COLARES, Antônio Gervásio. Integral formulae for spacelikehypersurfaces in conformally stationary spacetimes and applications. Proceedings of the Edinburg Mathematical Society, v. 46, n. 2, p. 465-488, 2003.http://www.repositorio.ufc.br/handle/riufc/4631In this paper we develop general Minkowski-type formulae for compact spacelike hypersurfaces immersed into conformally stationary spacetimes, that is, Lorentzian manifolds admitting a timelike conformal field. We apply them to the study of the umbilicity of compact spacelike hypersurfaces in terms of their r-mean curvatures. We derive several uniqueness results, for instance, compact spacelike hypersurfaces are umbilical if either some of their r-mean curvatures are linearly related or one of them is constant.HipersuperfíciesCampos vetoriaisCurvaturaIntegral formulae for spacelikehypersurfaces in conformally stationary spacetimes and applicationsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessengreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFCORIGINAL2003 _art_ljalias.pdf2003 _art_ljalias.pdfapplication/pdf243255http://repositorio.ufc.br/bitstream/riufc/4631/1/2003%20_art_ljalias.pdf6b40b40a0eec5c3a50eda40c6c57214aMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81786http://repositorio.ufc.br/bitstream/riufc/4631/2/license.txt8c4401d3d14722a7ca2d07c782a1aab3MD52riufc/46312023-10-31 11:38:21.697oai:repositorio.ufc.br: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Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2023-10-31T14:38:21Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false
dc.title.pt_BR.fl_str_mv Integral formulae for spacelikehypersurfaces in conformally stationary spacetimes and applications
title Integral formulae for spacelikehypersurfaces in conformally stationary spacetimes and applications
spellingShingle Integral formulae for spacelikehypersurfaces in conformally stationary spacetimes and applications
Alías, Luís J.
Hipersuperfícies
Campos vetoriais
Curvatura
title_short Integral formulae for spacelikehypersurfaces in conformally stationary spacetimes and applications
title_full Integral formulae for spacelikehypersurfaces in conformally stationary spacetimes and applications
title_fullStr Integral formulae for spacelikehypersurfaces in conformally stationary spacetimes and applications
title_full_unstemmed Integral formulae for spacelikehypersurfaces in conformally stationary spacetimes and applications
title_sort Integral formulae for spacelikehypersurfaces in conformally stationary spacetimes and applications
author Alías, Luís J.
author_facet Alías, Luís J.
Brasil Júnior, Aldir Chaves
Colares, Antônio Gervásio
author_role author
author2 Brasil Júnior, Aldir Chaves
Colares, Antônio Gervásio
author2_role author
author
dc.contributor.author.fl_str_mv Alías, Luís J.
Brasil Júnior, Aldir Chaves
Colares, Antônio Gervásio
dc.subject.por.fl_str_mv Hipersuperfícies
Campos vetoriais
Curvatura
topic Hipersuperfícies
Campos vetoriais
Curvatura
description In this paper we develop general Minkowski-type formulae for compact spacelike hypersurfaces immersed into conformally stationary spacetimes, that is, Lorentzian manifolds admitting a timelike conformal field. We apply them to the study of the umbilicity of compact spacelike hypersurfaces in terms of their r-mean curvatures. We derive several uniqueness results, for instance, compact spacelike hypersurfaces are umbilical if either some of their r-mean curvatures are linearly related or one of them is constant.
publishDate 2003
dc.date.issued.fl_str_mv 2003
dc.date.accessioned.fl_str_mv 2013-02-28T13:25:28Z
dc.date.available.fl_str_mv 2013-02-28T13:25:28Z
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.citation.fl_str_mv ALIÁS, Luis J. ; BRASIL JÚNIOR, Aldir Chaves ; COLARES, Antônio Gervásio. Integral formulae for spacelikehypersurfaces in conformally stationary spacetimes and applications. Proceedings of the Edinburg Mathematical Society, v. 46, n. 2, p. 465-488, 2003.
dc.identifier.uri.fl_str_mv http://www.repositorio.ufc.br/handle/riufc/4631
identifier_str_mv ALIÁS, Luis J. ; BRASIL JÚNIOR, Aldir Chaves ; COLARES, Antônio Gervásio. Integral formulae for spacelikehypersurfaces in conformally stationary spacetimes and applications. Proceedings of the Edinburg Mathematical Society, v. 46, n. 2, p. 465-488, 2003.
url http://www.repositorio.ufc.br/handle/riufc/4631
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.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)
bitstream.url.fl_str_mv http://repositorio.ufc.br/bitstream/riufc/4631/1/2003%20_art_ljalias.pdf
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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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