The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1
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| Formato: | Artículo científico |
| Lenguaje: | en |
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Academia Brasileira de Ciências
2008
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| _version_ | 1876432044372787200 |
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| author | Shuguo Shi |
| author_facet | Shuguo Shi |
| contents | The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1 Shuguo Shi Multidisciplinaria (Ciencias Naturales y Exactas) Monge Ampère equation duality property de Sitter Gauss map generalized Gauss map In this paper, we introduce the fourth fundamental forms for hypersurfaces in Hn+1 and space-like hypersurfacesin Sn+11 , and discuss the conformality of the normal Gauss map of the hypersurfaces in Hn+1 andSn+11 . Particularly, we discuss the surfaces with conformal normal Gauss map in H3 and S31 , and prove aduality property. We give aWeierstrass representation formula for space-like surfaces in S31 with conformalnormal Gauss map. We also state the similar results for time-like surfaces in S31 . Some examples of surfacesin S31 with conformal normal Gauss map are given and a fully nonlinear equation of Monge-Ampère typefor the graphs in S31 with conformal normal Gauss map is derived. 2008 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32780102 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.1 Vol.80 |
| format | Artículo científico |
| id | redalyc_32780102 |
| institution | Redalyc |
| language | en |
| publishDate | 2008 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1 Shuguo Shi Multidisciplinaria (Ciencias Naturales y Exactas) Monge Ampère equation duality property de Sitter Gauss map generalized Gauss map The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1 Shuguo Shi Multidisciplinaria (Ciencias Naturales y Exactas) Monge Ampère equation duality property de Sitter Gauss map generalized Gauss map In this paper, we introduce the fourth fundamental forms for hypersurfaces in Hn+1 and space-like hypersurfacesin Sn+11 , and discuss the conformality of the normal Gauss map of the hypersurfaces in Hn+1 andSn+11 . Particularly, we discuss the surfaces with conformal normal Gauss map in H3 and S31 , and prove aduality property. We give aWeierstrass representation formula for space-like surfaces in S31 with conformalnormal Gauss map. We also state the similar results for time-like surfaces in S31 . Some examples of surfacesin S31 with conformal normal Gauss map are given and a fully nonlinear equation of Monge-Ampère typefor the graphs in S31 with conformal normal Gauss map is derived. 2008 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32780102 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.1 Vol.80 |
| title | The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1 |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) Monge Ampère equation duality property de Sitter Gauss map generalized Gauss map |
| url | https://www.redalyc.org/articulo.oa?id=32780102 |