BI-ROTATIONAL HYPERSURFACE SATISFYING ?IIIx = Ax IN 4-SPACE

Abstract

We examine the bi-rotational hypersurface x = x(u, v, w) with the third Laplace-Beltrami operator in the four dimensional Euclidean space E-4. Giving the i-th curvatures of the hypersurface x, we obtain the third Laplace-Beltrami operator of the bi-rotational hypersurface satisfying Delta(III)x =Ax for some 4 x 4 matrix A.