Cheng-Yau Operator and Gauss Map of Rotational Hypersurfaces in 4-Space

Abstract

We consider rotational hypersurface in the four-dimensional Euclidean space E-4. We study the Gauss map G of rotational hypersurface in E-4 with respect to the so-called Cheng-Yau operator L-1 acting on the functions defined on the hypersurfaces. We obtain the classification theorem that the only rotational hypersurface with Gauss map G satisfying L-1 G = AG for some 4 x 4 matrix A are the hyperplanes, right circular hypercones, circular hypercylinders, and hyperspheres.