Ulisse dini-type helicoidal hypersurface 4-space

Abstract

We considerUlisse Dini-type helicoidal hypersurface in Euclidean 4-space E4.We give some basic notions of the fourdimensional Euclidean geometry in section 2.In section 3, we consider Ulisse Dini helicoidal hypersurface.We obtain Ulisse Dini-type helicoidal hypersurface, and calculate its curvatures in the last section.We calculatethe first and second fundamental forms, matrix of the shape operator S, Gaussian curvature K, and the mean curvature H of hypersurface M=M(u,v,w) in Euclidean 4-space E4.