The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1

Detalhes bibliográficos
Autor(a) principal: Shi,Shuguo
Data de Publicação: 2008
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=S0001-37652008000100002
Resumo: In this paper, we introduce the fourth fundamental forms for hypersurfaces in Hn+1 and space-like hypersurfaces in S1n+1, and discuss the conformality of the normal Gauss map of the hypersurfaces in Hn+1 and S1n+1. Particularly, we discuss the surfaces with conformal normal Gauss map in H³ and S³1, and prove a duality property. We give a Weierstrass representation formula for space-like surfaces in S³1 with conformal normal Gauss map. We also state the similar results for time-like surfaces in S³1. Some examples of surfaces in S³1 with conformal normal Gauss map are given and a fully nonlinear equation of Monge-Ampère type for the graphs in S³1 with conformal normal Gauss map is derived.
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spelling The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1fourth fundamental formconformal normal Gauss mapgeneralized Gauss mapduality propertyde Sitter Gauss mapMonge-Ampère equationIn this paper, we introduce the fourth fundamental forms for hypersurfaces in Hn+1 and space-like hypersurfaces in S1n+1, and discuss the conformality of the normal Gauss map of the hypersurfaces in Hn+1 and S1n+1. Particularly, we discuss the surfaces with conformal normal Gauss map in H³ and S³1, and prove a duality property. We give a Weierstrass representation formula for space-like surfaces in S³1 with conformal normal Gauss map. We also state the similar results for time-like surfaces in S³1. Some examples of surfaces in S³1 with conformal normal Gauss map are given and a fully nonlinear equation of Monge-Ampère type for the graphs in S³1 with conformal normal Gauss map is derived.Academia Brasileira de Ciências2008-03-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652008000100002Anais da Academia Brasileira de Ciências v.80 n.1 2008reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652008000100002info:eu-repo/semantics/openAccessShi,Shuguoeng2008-03-10T00:00:00Zoai:scielo:S0001-37652008000100002Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2008-03-10T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1
title The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1
spellingShingle The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1
Shi,Shuguo
fourth fundamental form
conformal normal Gauss map
generalized Gauss map
duality property
de Sitter Gauss map
Monge-Ampère equation
title_short The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1
title_full The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1
title_fullStr The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1
title_full_unstemmed The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1
title_sort The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1
author Shi,Shuguo
author_facet Shi,Shuguo
author_role author
dc.contributor.author.fl_str_mv Shi,Shuguo
dc.subject.por.fl_str_mv fourth fundamental form
conformal normal Gauss map
generalized Gauss map
duality property
de Sitter Gauss map
Monge-Ampère equation
topic fourth fundamental form
conformal normal Gauss map
generalized Gauss map
duality property
de Sitter Gauss map
Monge-Ampère equation
description In this paper, we introduce the fourth fundamental forms for hypersurfaces in Hn+1 and space-like hypersurfaces in S1n+1, and discuss the conformality of the normal Gauss map of the hypersurfaces in Hn+1 and S1n+1. Particularly, we discuss the surfaces with conformal normal Gauss map in H³ and S³1, and prove a duality property. We give a Weierstrass representation formula for space-like surfaces in S³1 with conformal normal Gauss map. We also state the similar results for time-like surfaces in S³1. Some examples of surfaces in S³1 with conformal normal Gauss map are given and a fully nonlinear equation of Monge-Ampère type for the graphs in S³1 with conformal normal Gauss map is derived.
publishDate 2008
dc.date.none.fl_str_mv 2008-03-01
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=S0001-37652008000100002
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652008000100002
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652008000100002
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.80 n.1 2008
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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