EAP - Proceedings of the Estonian Academy of Sciences

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proceedings
of the estonian academy of sciences

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Hypersurfaces with pointwise 1-type Gauss map in Lorentz–Minkowski space; 146–161

PDF | doi: 10.3176/proc.2009.3.02

Author

Uğur Dursun

Abstract

Hypersurfaces of a Lorentz–Minkowski space Lⁿ⁺¹ with pointwise 1-type Gauss map are characterized. We prove that an oriented hypersurface M_q in Lⁿ⁺¹ has pointwise 1-type Gauss map of the first kind if and only if M_q has constant mean curvature and conclude that all oriented isoparametric hypersurfaces in Lⁿ⁺¹ have 1-type Gauss map. Then we classify rational rotation hypersurfaces of Lⁿ⁺¹ with pointwise 1-type Gauss map and give some examples.

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