Local isometry of the generalized helicoidal surfaces family in 4-space

Abstract

In this paper, we define generalized helicoidal surface in the four dimensional Euclidean space ${\mathbb{E}}^{4}$. We compute two normals and the curvatures of helicoidal surface. Finally, we obtain local isometry from generalized helicoidal surface to the generalized rotational surface by applying Bour's theorem in ${\mathbb{E}}^{4}$.