Cheng-yau operator and gauss map of rotational hypersurfaces in the four dimensional euclidean space

Abstract

We consider rotational hypersurface in the four dimensional Euclidean space 4E. We study the Gauss map G of rotational hypersurface in 4E with respect to the so-called Cheng-Yau operator 1L acting on the functions defined on the hypersurfaces. We obtain the classification theorem that the only rotational hypersurface with Gauss map G satisfying 1L GAG= for some 4×4 matrix A.