Twisted Hypersurfaces in Euclidean 5-Space

Author:

Li Yanlin12ORCID,Güler Erhan3ORCID

Affiliation:

1. School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China

2. Key Laboratory of Cryptography of Zhejiang Province, Hangzhou Normal University, Hangzhou 311121, China

3. Department of Mathematics, Faculty of Sciences, Bartın University, Kutlubey Campus, Bartın 74100, Turkey

Abstract

The twisted hypersurfaces x with the (0,0,0,0,1) rotating axis in five-dimensional Euclidean space E5 is considered. The fundamental forms, the Gauss map, and the shape operator of x are calculated. In E5, describing the curvatures by using the Cayley–Hamilton theorem, the curvatures of hypersurfaces x are obtained. The solutions of differential equations of the curvatures of the hypersurfaces are open problems. The umbilically and minimality conditions to the curvatures of x are determined. Additionally, the Laplace–Beltrami operator relation of x is given.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

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