| Registro completo |
| Provedor de dados: |
Anais da ABC (AABC)
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| País: |
Brazil
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| Título: |
The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1
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| Autores: |
Shi,Shuguo
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| Data: |
2008-03-01
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| Ano: |
2008
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| Palavras-chave: |
Fourth fundamental form
Conformal normal Gauss map
Generalized Gauss map
Duality property
De Sitter Gauss map
Monge-Ampère equation
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| 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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| Tipo: |
Info:eu-repo/semantics/article
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| Idioma: |
Inglês
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| Identificador: |
http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652008000100002
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| Editor: |
Academia Brasileira de Ciências
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| Relação: |
10.1590/S0001-37652008000100002
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| Formato: |
text/html
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| Fonte: |
Anais da Academia Brasileira de Ciências v.80 n.1 2008
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| Direitos: |
info:eu-repo/semantics/openAccess
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