Analyzing geometric isometries of helical surfaces in five-dimensional Euclidean space

Abstract

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