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

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GÜLER E., Turgay N. C.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.16, no.3, 2019 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 16 Issue: 3
• Publication Date: 2019
• Doi Number: 10.1007/s00009-019-1333-y
• Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Istanbul Technical University Affiliated: Yes

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.