Twisted Hypersurfaces in Euclidean 5-Space

Yanlin Li () and Erhan Güler
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Yanlin Li: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Erhan Güler: Department of Mathematics, Faculty of Sciences, Bartın University, Kutlubey Campus, Bartın 74100, Turkey

Mathematics, 2023, vol. 11, issue 22, 1-17

Abstract: The twisted hypersurfaces x with the ( 0 , 0 , 0 , 0 , 1 ) rotating axis in five-dimensional Euclidean space E 5 is considered. The fundamental forms, the Gauss map, and the shape operator of x are calculated. In E 5 , 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.

Keywords: Euclidean five-space; twisted hypersurfaces family; Gauss map; mean curvature; Gauss–Kronecker curvature; Cayley–Hamilton theorem; Laplace–Beltrami operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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