Translation hypersurfaces with constant curvature in 4-dimensional isotropic space

2017/11/24 by Aydin, Muhittin Evren, Ogrenmis, Alper Osman
#53A10 #53A35 #53B25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.09051

Abstract

There exist four non-equivalent types of the translation hypersurfaces in the 4-dimensional isotropic space \mathbbI⁴ generated by translating the curves lying in perpendicular k-planes (k=2,3), 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 \citeAO. The present study concerns such hypersurfaces in \mathbbI⁴ of other three types.

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• Classifications of translation surfaces in isotropic geometry with constant curvature
• Affine translation hypersurfaces in Euclidean and isotropic spaces
• Translation hypersurfaces with constant Sr curvature in the Euclidean space
• Constant curvature translation surfaces in Galilean 3-space
• Translation surfaces in Euclidean space with constant Gaussian curvature