HYPERSPHERE SATISFYING ?x =Ax IN 4-SPACE

Abstract

We consider hypersphere x = x(u, v, w) in the four dimensional Euclidean space. We calculate the Gauss map, and the curvatures of it. Moreover, we obtain the Laplace-Beltrami operator the hypersphere satisfying ?x =Ax, where A ? Mat (4, 4). © 2022 Elsevier B.V., All rights reserved.