The Gauss Map and the Third Laplace-Beltrami Operator of the Rotational Hypersurface in 4-Space

Abstract

We study and examine the rotational hypersurface and its Gauss map in Euclidean four-space E-4. We calculate the Gauss map, the mean curvature and the Gaussian curvature of the rotational hypersurface and obtain some results. Then, we introduce the third Laplace-Beltrami operator. Moreover, we calculate the third Laplace-Beltrami operator of the rotational hypersurface in E-4. We also draw some figures of the rotational hypersurface.