Abstract
In this paper, we study the problem of constructing a family of surfaces (surface pencils) from a given curve in [Formula: see text]-dimensional Euclidean space [Formula: see text]. We have shown that the generalized rotation surfaces in [Formula: see text] 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 [Formula: see text].
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