On translation surfaces in 4-dimensional Euclidean space

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

ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA, cilt.20, sa.2, ss.123-133, 2016 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 2
  • Basım Tarihi: 2016
  • Doi Numarası: 10.12697/acutm.2016.20.11
  • Dergi Adı: ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.123-133
  • Anahtar Kelimeler: Translation surface, mean curvature, Gaussian curvature, second fundamental map, FORM
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.