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On translation surfaces in 4-dimensional euclidean space

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Arslan, Kadri
Bulca, Betul

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Bayram, Bengü
Öztürk, Günay

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Univ Tartu Press

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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.

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Form, Translation surface, Mean curvature, Gaussian curvature, Second fundamental map, Science & technology, Physical sciences, Mathematics

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