Rigidity theorems of Clifford Torus

Detalhes bibliográficos
Autor(a) principal: SOUSA JR.,LUIZ A. M.
Data de Publicação: 2001
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=S0001-37652001000300003
Resumo: Let M be an n-dimensional closed minimally immersed hypersurface in the unit sphere Sn + 1. Assume in addition that M has constant scalar curvature or constant Gauss-Kronecker curvature. In this note we announce that if M has (n - 1) principal curvatures with the same sign everywhere, then M is isometric to a Clifford Torus <img src="http:/img/fbpe/aabc/v73n3/03ab.gif" alt="03ab.gif (725 bytes)" align="middle">.
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spelling Rigidity theorems of Clifford Torusminimal hypersurfacesscalar curvatureprincipal curvaturesClifford TorusLet M be an n-dimensional closed minimally immersed hypersurface in the unit sphere Sn + 1. Assume in addition that M has constant scalar curvature or constant Gauss-Kronecker curvature. In this note we announce that if M has (n - 1) principal curvatures with the same sign everywhere, then M is isometric to a Clifford Torus <img src="http:/img/fbpe/aabc/v73n3/03ab.gif" alt="03ab.gif (725 bytes)" align="middle">.Academia Brasileira de Ciências2001-09-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652001000300003Anais da Academia Brasileira de Ciências v.73 n.3 2001reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652001000300003info:eu-repo/semantics/openAccessSOUSA JR.,LUIZ A. M.eng2001-10-09T00:00:00Zoai:scielo:S0001-37652001000300003Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2001-10-09T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv Rigidity theorems of Clifford Torus
title Rigidity theorems of Clifford Torus
spellingShingle Rigidity theorems of Clifford Torus
SOUSA JR.,LUIZ A. M.
minimal hypersurfaces
scalar curvature
principal curvatures
Clifford Torus
title_short Rigidity theorems of Clifford Torus
title_full Rigidity theorems of Clifford Torus
title_fullStr Rigidity theorems of Clifford Torus
title_full_unstemmed Rigidity theorems of Clifford Torus
title_sort Rigidity theorems of Clifford Torus
author SOUSA JR.,LUIZ A. M.
author_facet SOUSA JR.,LUIZ A. M.
author_role author
dc.contributor.author.fl_str_mv SOUSA JR.,LUIZ A. M.
dc.subject.por.fl_str_mv minimal hypersurfaces
scalar curvature
principal curvatures
Clifford Torus
topic minimal hypersurfaces
scalar curvature
principal curvatures
Clifford Torus
description Let M be an n-dimensional closed minimally immersed hypersurface in the unit sphere Sn + 1. Assume in addition that M has constant scalar curvature or constant Gauss-Kronecker curvature. In this note we announce that if M has (n - 1) principal curvatures with the same sign everywhere, then M is isometric to a Clifford Torus <img src="http:/img/fbpe/aabc/v73n3/03ab.gif" alt="03ab.gif (725 bytes)" align="middle">.
publishDate 2001
dc.date.none.fl_str_mv 2001-09-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652001000300003
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652001000300003
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652001000300003
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.73 n.3 2001
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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