On the translation hypersurfaces with Gauss map G satisfying ΔG=AG

G. Aydin Sekerci, S. Sevinc, A.C. Cöken
2019 Miskolc Mathematical Notes  
It is a known fact that a translation hypersurface is obtained by combination of any three curves in the 4-dimensional Euclidean space. We examine a special situation where the Gauss map of a translation hypersurface satisfies the condition G D AG where represents the Laplace operator and A is a 4 4-real matrix. Our result is that such a translation hypersurface is one of the following three hypersurfaces: the hypersurface of translation surface and a constant vector along this surface, the
more » ... is surface, the hyperplane, the hypersurface˙ R where˙is a translation surface.
doi:10.18514/mmn.2019.3021 fatcat:bkghdt354vbn7esak53z6t664y