Generalized constant ratio hypersurfaces in Euclidean spaces

Abstract

In this paper, we study generalized constant ratio (GCR) hypersurfaces in Euclidean spaces. We mainly focus on the hypersurfaces in ${\mathbb{E}}^4$. First, we deal with $\delta (2)$-ideal GCR hypersurfaces. Then, we study on hypersurfaces with constant (first) mean curvature. Finally, we obtain the complete classification of GCR hypersurfaces with vanishing Gauss-Kronecker curvature. We also give some explicit examples. Keywords: Generalized constant ratio submanifolds, $\delta (r)$-invariant hypersurfaces, constant mean curvature, Gauss-Kronecker curvature

References in corpus (1)

• On certain surfaces in the Euclidean space ${\mathbb{E}}^3$