The hypersurfaces with conformal normal Gauss map in H^n+1 and S_{1}^{n+1}

Details The hypersurfaces with conformal normal Gauss map in H^n+1 and S_{1}^{n+1} The hypersurfaces with conformal normal Gauss map in H^n+1 and S_{1}^{n+1}

2006-10-31

arxiv.org/abs/math/0610964v2

Mathematics

Differential Geometry

18 pages

Scientific paper

In this paper we introduce the fourth fundamental form for the hypersurfaces in $H^{n+1}$ and the space-like hypersurfaces in $S_{1}^{n+1}$ and discuss the conformality of the normal Gauss maps of the hypersurfaces in $H^{n+1}$ and $S_{1}^{n+1}$. Particularly, we discuss the surfaces with conformal normal Gauss maps in $H^{3}$ and $S_{1}^{3}$ and prove a duality property. We give the Weierstrass representation formula for the space-like surfaces in $S_{1}^{3}$ with conformal normal Gauss maps. We also state the similar results for the time-like surfaces in $S_{1}^{3}.$

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