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| Format: | Artículo científico |
| Language: | en |
| Published: |
Academia Brasileira de Ciências
2008
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| Online Access: | https://www.redalyc.org/articulo.oa?id=32780102 |
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Table of 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