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

Abstract

Hypersurfaces of a Lorentzâ Minkowski space Ln+1 with pointwise 1-type Gauss map are characterized. We prove that an oriented hypersurface Mq in Ln+1 has pointwise 1-type Gauss map of the first kind if and only if Mq 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.