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

Anais da Academia Brasileira de Ciências

Shuguo Shi¹ 

[1] ,Shandong University School of Mathematics and System SciencesP.R. ,China

关键词: fourth fundamental form;    conformal normal Gauss map;    generalized Gauss map;    duality property;    de Sitter Gauss map;    Monge-Ampère equation;    quarta forma fundamental;    aplicação normal de Gauss conforme;    aplicação de Gauss generalizada;    propriedade de dualidade;    aplicação de Gauss de Sitter;    equação de Monge-Ampère;   

DOI  :  10.1590/S0001-37652008000100002

来源: SciELO

【 摘 要 】

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.

【 授权许可】

CC BY   
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