RIGHT CONOID HYPERSURFACES IN FOUR-SPACE

Abstract

The right conoid hypersurfaces in the four-dimensional Euclidean space E4 are introduced. The matrices corresponding to the fundamental form, Gauss map, and shape operator of these hypersurfaces are calculated. By utilizing the Cayley-Hamilton theorem, the curvatures of these specific hypersurfaces are determined. Furthermore, the conditions for minimality are presented. Additionally, the Laplace-Beltrami oper-ator of this family is computed, and some examples are provided.