Investigating Helical Hypersurfaces Within 7-Dimensional Euclidean Space

Abstract

Differential geometry of a kind of helical hypersurface family that depends on six parameters within the seven-dimensional Euclidean space is explored. The curvatures of these hypersurfaces are determined, and their minimality is examined, along with illustrative examples being provided. Lastly, the Laplace-Beltrami operator for that kind of hypersurfaces is calculated.