On translation surfaces in 4-dimensional Euclidean space

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 Bézier surface in E 4 to become a translation surface.

Rotational Hypersurfaces in Euclidean 4-Space with Density

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Semi-parallel and harmonic surfaces in semi-Euclidean 4-space with index 2

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