Rotation hypersurfaces in $\mathbb{S}^n\times\mathbb{R}$ and $\mathbb{H}^n\times\mathbb{R}$

Abstract

We introduce the notion of rotation hypersurfaces of $\mathbb{S}^n\times\mathbb{R}$and $\mathbb{H}^n\times\mathbb{R}$ and we prove a criterium for a hypersurface ofone of these spaces to be a rotation hypersurface. Moreover, weclassify minimal rotation hypersurfaces, flat rotation hypersurfacesand rotation hypersurfaces which are normally flat in the Euclideanresp. Lorentzian space containing $\mathbb{S}^n\times\mathbb{R}$ resp.$\mathbb{H}^n\times\mathbb{R}$.