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


GÜLER E., Turgay N. C.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.16, no.3, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.1007/s00009-019-1333-y
  • Title of Journal : MEDITERRANEAN JOURNAL OF MATHEMATICS

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.