Birotational hypersurface and the second Laplace-Beltrami operator in the four dimensional Euclidean space E4

Abstract

We consider the birotational hypersurface x(u, v, w) with the second Laplace-Beltrami operator in the four dimensional Euclidean space E-4. We give the i -th curvatures of x. In addition, we compute the second Laplace-Beltrami operator of the birotational hypersurface satisfying Delta(II) x =Ax for some 4 x 4 matrix A.