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


GÜLER E., Turgay N. C.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.16, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 16 Konu: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s00009-019-1333-y
  • Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS

Özet

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.