A Hypersurfaces of Revolution Family in the Five-Dimensional Pseudo-Euclidean Space E 2 5

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, 74100 Bartın, Turkey

Mathematics, 2023, vol. 11, issue 15, 1-12

Abstract: We present a family of hypersurfaces of revolution distinguished by four parameters in the five-dimensional pseudo-Euclidean space E 2 5 . The matrices corresponding to the fundamental form, Gauss map, and shape operator of this family are computed. By utilizing the Cayley–Hamilton theorem, we determine the curvatures of the specific family. Furthermore, we establish the criteria for maximality within this framework. Additionally, we reveal the relationship between the Laplace–Beltrami operator of the family and a 5 × 5 matrix.

Keywords: pseudo-Euclidean 5-space; hypersurfaces of revolution family; Gauss map; shape operator: curvature; Laplace–Beltrami operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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