On translation surfaces in 4-dimensional Euclidean space

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

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

• Publication Type: Article / Article
• Volume: 20 Issue: 2
• Publication Date: 2016
• Doi Number: 10.12697/acutm.2016.20.11
• Journal Name: ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA
• Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
• Page Numbers: pp.123-133
• Open Archive Collection: AVESIS Open Access Collection
• Kocaeli University Affiliated: Yes

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.