ON THE TRANSLATION HYPERSURFACES WITH GAUSS MAP G SATISFYING Delta G = AG


Sekerci G. A. , Sevinc S. , ÇÖKEN A. C.

MISKOLC MATHEMATICAL NOTES, cilt.20, ss.1215-1225, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 20 Konu: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.18514/mmn.2019.3021
  • Dergi Adı: MISKOLC MATHEMATICAL NOTES
  • Sayfa Sayıları: ss.1215-1225

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.