ON THE TRANSLATION HYPERSURFACES WITH GAUSS MAP G SATISFYING Delta G = AG
MISKOLC MATHEMATICAL NOTES, vol.20, no.2, pp.1215-1225, 2019 (SCI-Expanded)
- Publication Type: Article / Article
- Volume: 20 Issue: 2
- Publication Date: 2019
- Doi Number: 10.18514/mmn.2019.3021
- Journal Name: MISKOLC MATHEMATICAL NOTES
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.1215-1225
- Keywords: translation hypersurface, Gauss map, Euclidean space, SURFACES
- Open Archive Collection: AVESIS Open Access Collection
- Akdeniz University Affiliated: Yes
Abstract
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 Delta G = AG where Delta represents the Laplace operator and A is a 4 x 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 hyperplane, the hypersurface Sigma x R where Sigma is a translation surface.