Surface Pencils in Euclidean 4-space $\mathbb{E}^{4}$

Abstract

In the present paper we study the problem of constructing a family of surfaces (surface pencils) from a given curve in 4-dimensional Euclidean space $\mathbb{E}^{4}$. We have shown that generalized rotation surfaces in $\mathbb{E}^{4}$ are the special type of surface pencils. Further, the curvature properties of these surfaces are investigated. Finally, we give some examples of flat surface pencils in $\mathbb{E}^{4}$.