Rotational Hypersurfaces Satisfying ΔIR = AR in the Four-Dimensional Euclidean Space

Abstract

In this study, rotational hypersurfaces in the 4-dimensional Euclidean space are discussed. Some relations of curvatures of hypersurfaces are given, such as the mean, Gaussian, and their minimality and flatness. In addition, Laplace-Beltrami operator has been defined for 4-dimensional hypersurfaces depending on the first fundamental form. Moreover, it is shown that each element of the 4 x 4 order matrix A, which satisfies the condition Delta R-I = AR, is zero, that is, the rotational hypersurface R is minimal.