Abstract
In this article we investigate Vranceanu rotation surfaces with pointwise 1- type Gauss map in Euclidean 4-space \( \mathbb{E}^4 \). We show that a Vranceanu rotation surface M has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficent conditions for Vranceanu rotation surface to have pointwise 1-type Gauss map.
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