Abstract:In this paper, we introduce the fourth fundamental forms for hypersurfaces in H n+1 and space-like hypersurfaces in S n+1 1 , and discuss the conformality of the normal Gauss map of the hypersurfaces in H n+1 and S n+11 . Particularly, we discuss the surfaces with conformal normal Gauss map in H 3 and S 3 1 , and prove a duality property. We give a Weierstrass representation formula for space-like surfaces in S 3 1 with conformal normal Gauss map. We also state the similar results for time-like surfaces in S 3… Show more
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