A Hypersurfaces of Revolution Family in the Five-Dimensional Pseudo-Euclidean Space E25

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 5x5 matrix.