ROTATIONAL HYPERSURFACES CONSTRUCTED BY DOUBLE ROTATION IN FIVE DIMENSIONAL EUCLIDEAN SPACE E5

Abstract

We introduce the rotational hypersurface x = x(u, v, s, t) constructed by double rotation in five dimensional Euclidean space E5. We reveal the first and the second fundamental form matrices, Gauss map, shape operator matrix of x. Additionally, defining the i-th curva-tures of any hypersurface via Cayley-Hamilton theorem, we compute the curvatures of the rotational hypersurface x. We give some relations of the mean and Gauss-Kronecker curvatures of x. In addition, we reveal increment x =Ax, where A is the 5 x 5 matrix in E5.