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

Abstract

In the context of five-dimensional Euclidean space E5, the definition of the helical surface is established. Its geometric attributes are elucidated by calculating three normals. Subsequently, Bour?s theorem within E5 is employed to determine an isometric mapping among helical-rotational surfaces, contributing to a better understanding of their structural interplay.