Cheng-yau operator and gauss map of rotational hypersurfaces in the four dimensional euclidean space - Güler, Erhan; Turgay, Nurettin Cenk (Manisa Celal Bayar University, 2018)
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.
Keywords: Euclidean spaces; Cheng-yau operator; Finite type mappings; Rotational hypersurfaces