ON THE TRANSLATION HYPERSURFACES WITH GAUSS MAP G SATISFYING Delta G = AG
MISKOLC MATHEMATICAL NOTES, cilt.20, sa.2, ss.1215-1225, 2019 (SCI-Expanded)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 20 Sayı: 2
- Basım Tarihi: 2019
- Doi Numarası: 10.18514/mmn.2019.3021
- Dergi Adı: MISKOLC MATHEMATICAL NOTES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1215-1225
- Anahtar Kelimeler: translation hypersurface, Gauss map, Euclidean space, SURFACES
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Akdeniz Üniversitesi Adresli: Evet
Özet
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.