Abstract
In the present paper we consider weak biharmonic rotational surfaces in Euclidean 4-space E⁴. We have proved that the general rotational surface of parallel mean curvature vector field is weak biharmonic then either it is minimal or a constant mean curvature. Further, we show that if Vranceanu surface of constant mean curvature is weak-biharmonic then it is a Clifford torus in E⁴.
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