Translation hypersurfaces with constant curvature in 4-dimensional isotropic space

Abstract

There exist four non-equivalent types of the translation hypersurfaces in the 4-dimensional isotropic space ${\mathbb{I}}^4$ generated by translating the curves lying in perpendicular $k-$planes $\left(k=2,3\right)$, due to its absolute figure. In arbitrary dimensional case; constant Gauss-Kronecker and mean curvature translation hypersurfaces of type 1, i.e. the hypersurfaces whose the translating curves lie in perpendicular isotropic $2-$planes, were investigated by the same authors in \cite{AO}. The present study concerns such hypersurfaces in ${\mathbb{I}}^4$ of other three types.