HONAM MATHEMATICAL JOURNAL, cilt.44, sa.2, ss.219-230, 2022 (ESCI)
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.