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


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

MISKOLC MATHEMATICAL NOTES, vol.20, no.2, pp.1215-1225, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.18514/mmn.2019.3021
  • Title of Journal : MISKOLC MATHEMATICAL NOTES
  • Page Numbers: pp.1215-1225

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.