On complete spacelike hypersurfaces with constant scalar curvature in the de Sitter space

Bibliographic Details
Main Author: BRASIL JR,ALDIR
Publication Date: 2000
Other Authors: COLARES,A. GERVASIO
Format: Article
Language: eng
Source: Anais da Academia Brasileira de Ciências (Online)
Download full: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652000000400001
Summary: Let Mn be a complete spacelike hypersurface with constant normalized scalar curvature R in the de Sitter Space S1n + 1. Let H the mean curvature and suppose that <img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img1.gif" ALT="$ \overline{R}$"> = (R - 1) > 0 and <img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img1.gif" ALT="$ \overline{R}$"> <= sup H² <= C<img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img3.gif" ALT="$\scriptstyle \overline{R}$">, where C<img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img3.gif" ALT="$\scriptstyle \overline{R}$"> is a constant depending only on R and n. It is proved that either sup H² = <img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img1.gif" ALT="$ \overline{R}$"> and Mn is totally umbilical, or sup H² = C<img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img3.gif" ALT="$\scriptstyle \overline{R}$"> and Mn is the hyperbolic cylinder H¹(1 - coth²r) x Sn - 1 (1 - tanh²r).
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spelling On complete spacelike hypersurfaces with constant scalar curvature in the de Sitter spacehyperbolic cylinderspacelike hypersurfacesde Sitter spaceLet Mn be a complete spacelike hypersurface with constant normalized scalar curvature R in the de Sitter Space S1n + 1. Let H the mean curvature and suppose that <img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img1.gif" ALT="$ \overline{R}$"> = (R - 1) > 0 and <img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img1.gif" ALT="$ \overline{R}$"> <= sup H² <= C<img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img3.gif" ALT="$\scriptstyle \overline{R}$">, where C<img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img3.gif" ALT="$\scriptstyle \overline{R}$"> is a constant depending only on R and n. It is proved that either sup H² = <img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img1.gif" ALT="$ \overline{R}$"> and Mn is totally umbilical, or sup H² = C<img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img3.gif" ALT="$\scriptstyle \overline{R}$"> and Mn is the hyperbolic cylinder H¹(1 - coth²r) x Sn - 1 (1 - tanh²r).Academia Brasileira de Ciências2000-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652000000400001Anais da Academia Brasileira de Ciências v.72 n.4 2000reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652000000400001info:eu-repo/semantics/openAccessBRASIL JR,ALDIRCOLARES,A. GERVASIOeng2001-01-05T00:00:00Zoai:scielo:S0001-37652000000400001Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2001-01-05T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv On complete spacelike hypersurfaces with constant scalar curvature in the de Sitter space
title On complete spacelike hypersurfaces with constant scalar curvature in the de Sitter space
spellingShingle On complete spacelike hypersurfaces with constant scalar curvature in the de Sitter space
BRASIL JR,ALDIR
hyperbolic cylinder
spacelike hypersurfaces
de Sitter space
title_short On complete spacelike hypersurfaces with constant scalar curvature in the de Sitter space
title_full On complete spacelike hypersurfaces with constant scalar curvature in the de Sitter space
title_fullStr On complete spacelike hypersurfaces with constant scalar curvature in the de Sitter space
title_full_unstemmed On complete spacelike hypersurfaces with constant scalar curvature in the de Sitter space
title_sort On complete spacelike hypersurfaces with constant scalar curvature in the de Sitter space
author BRASIL JR,ALDIR
author_facet BRASIL JR,ALDIR
COLARES,A. GERVASIO
author_role author
author2 COLARES,A. GERVASIO
author2_role author
dc.contributor.author.fl_str_mv BRASIL JR,ALDIR
COLARES,A. GERVASIO
dc.subject.por.fl_str_mv hyperbolic cylinder
spacelike hypersurfaces
de Sitter space
topic hyperbolic cylinder
spacelike hypersurfaces
de Sitter space
description Let Mn be a complete spacelike hypersurface with constant normalized scalar curvature R in the de Sitter Space S1n + 1. Let H the mean curvature and suppose that <img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img1.gif" ALT="$ \overline{R}$"> = (R - 1) > 0 and <img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img1.gif" ALT="$ \overline{R}$"> <= sup H² <= C<img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img3.gif" ALT="$\scriptstyle \overline{R}$">, where C<img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img3.gif" ALT="$\scriptstyle \overline{R}$"> is a constant depending only on R and n. It is proved that either sup H² = <img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img1.gif" ALT="$ \overline{R}$"> and Mn is totally umbilical, or sup H² = C<img ALIGN="BOTTOM" BORDER="0" SRC="http:/img/fbpe/aabc/v72n4/0045img3.gif" ALT="$\scriptstyle \overline{R}$"> and Mn is the hyperbolic cylinder H¹(1 - coth²r) x Sn - 1 (1 - tanh²r).
publishDate 2000
dc.date.none.fl_str_mv 2000-12-01
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=S0001-37652000000400001
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652000000400001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652000000400001
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.72 n.4 2000
reponame:Anais da Academia Brasileira de Ciências (Online)
instname:Academia Brasileira de Ciências (ABC)
instacron:ABC
instname_str Academia Brasileira de Ciências (ABC)
instacron_str ABC
institution ABC
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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