Hypersurfaces with pointwise 1-type Gauss map in Lorentz-Minkowski space


Dursun U.

PROCEEDINGS OF THE ESTONIAN ACADEMY OF SCIENCES, vol.58, no.3, pp.146-161, 2009 (SCI-Expanded) identifier identifier

Abstract

Hypersurfaces of a Lorentz-Minkowski space L(n+1) with pointwise 1-type Gauss map are characterized. We prove that an oriented hypersurface M(q) in L(n+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 L(n+1) have 1-type Gauss map. Then we classify rational rotation hypersurfaces of L(n+1) with pointwise 1-type Gauss map and give some examples.