RIGHT CONOID HYPERSURFACES IN FOUR-SPACE

Abstract

The right conoid hypersurfaces in the four-dimensional Euclidean space $\mathbb{E}^{4}$ 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 operator of this family is computed, and some examples are provided.