In the present study we consider generalized rotation surfaces imbedded in an Euclidean space of four dimensions. We also give some special examples of these surfaces in E 4 . Further, the curvature properties of these surfaces are investigated. We give necessary and sufficient conditions for generalized rotation surfaces to become pseudo-umbilical. We also show that every general rotation surface is Chen surface in E 4 . Finally we give some examples of generalized rotation surfaces in E 4 .Mathematics Subject Classification (2010). Primary 53C40; Secondary 53C42.

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.

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In this study, we consider Tzitzeica curves (Tz-curves) in Euclidean 3-space E^3. We characterize such curves according to their curvatures. We show that there is no Tz-curve with constant curvatures (W-curves). We consider Salkowski (TC-curve) and Anti-Salkowski curves.

In the present study, we consider canal surfaces imbedded in an Euclidean space of four dimensions. The curvature properties of these surface are investigated with respect to the variation of the normal vectors and curvature ellipse. We also give some special examples of canal surfaces in E^4. Further, we give necessary and sufficient condition for canal surfaces in E^4 to become superconformal. Finally, the visualization of the projections of canal surfaces in E^3 are presented.