Surface pencils in Euclidean 4-space 𝔼4

Abstract

In this paper, we study the problem of constructing a family of surfaces (surface pencils) from a given curve in 4-dimensional Euclidean space E 4 . We have shown that the generalized rotation surfaces in 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 E 4 .