On translation surfaces in 4-dimensional Euclidean space


ARSLAN K. , Bayram B., BULCA B. , Ozturk G.

ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA, vol.20, no.2, pp.123-133, 2016 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.12697/acutm.2016.20.11
  • Title of Journal : ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA
  • Page Numbers: pp.123-133
  • Keywords: Translation surface, mean curvature, Gaussian curvature, second fundamental map, FORM

Abstract

We consider translation surfaces in Euclidean spaces. Firstly, we give some results of translation surfaces in the 3-dimensional Euclidean space E-3. Further, we consider translation surfaces in the 4-dimensional Euclidean space E-4. We prove that a translation surface is flat in E-4 if and only if it is either a hyperplane or a hypercylinder. Finally we give necessary and sufficient condition for a quadratic triangular Bezier surface in E-4 to become a translation surface.