A Hypersurfaces of Revolution Family in the Five-Dimensional Pseudo-Euclidean Space E25 - Li, Yanlin; Guler, Erhan (Mdpi, 2023)
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 5x5 matrix.
Keywords: Pseudo-Euclidean 5-Space; Hypersurfaces Of Revolution Family; Gauss Map; Shape Operator; Curvature; Laplace-Beltrami Operator