Translation hypersurfaces with constant curvature in 4-dimensional isotropic space

Muhittin Evren Aydin; Alper Osman Ogrenmis

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arXiv · 1711.09051

Translation hypersurfaces with constant curvature in 4-dimensional isotropic space

Muhittin Evren Aydin·Alper Osman Ogrenmis

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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.

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Muhittin Evren Aydin, Alper Osman Ogrenmis. 2017-11-24. Translation hypersurfaces with constant curvature in 4-dimensional isotropic space. https://arxiv.org/abs/1711.09051

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