BI-ROTATIONAL HYPERSURFACE WITH ?x = Ax IN 4-SPACE

Abstract

We introduce the bi-rotational hypersurface x(u, v, w) in the four dimen-sional Euclidean geometry E4. We obtain the i-th curvatures of the hypersurface. More-over, we consider the Laplace-Beltrami operator of the bi-rotational hypersurface sat-isfying delta x =Ax for some 4 x 4 matrix A.