Surfaces Given with the Monge Patch in $\mathbb{E}^{4}$

In the present paper we consider the surfaces in the Euclidean 4-space $\mathbb{E}^{4}$ given with a Monge patch $z=f(u,v)$, $w=g(u,v)$ and study the curvature properties of these surfaces. We also give some special examples of these surfaces first defined by Yu. Aminov. Finally, we prove that every Aminov surface is a non-trivial Chen surface.