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 ${\mathbb{E}}^4$.

9 pages