Analyzing Geometric Isometries of Helical Surfaces in Five-Dimensional Euclidean Space

Abstract

In the context of five-dimensional Euclidean space $\mathbb{E}^5$, the definition of the helical surface is established. Its geometric attributes are elucidated by calculating three normals. Subsequently, Bour's theorem within $\mathbb{E}^5$ is employed to determine an isometric mapping among helical-rotational surfaces, contributing to a better understanding of their structural interplay.