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Twisted Hypersurfaces in Euclidean 5-Space

Author

Listed:
  • Yanlin Li

    (School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
    Key Laboratory of Cryptography of Zhejiang Province, Hangzhou Normal University, Hangzhou 311121, China
    These authors contributed equally to this work.)

  • Erhan Güler

    (Department of Mathematics, Faculty of Sciences, Bartın University, Kutlubey Campus, Bartın 74100, Turkey
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Yanlin Li & Erhan Güler, 2023. "Twisted Hypersurfaces in Euclidean 5-Space," Mathematics, MDPI, vol. 11(22), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4612-:d:1278035
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