Classification of separable hypersurfaces with constant sectional curvature

Abstract

In this paper, we give a full classification of the separable hypersurfaces of constant sectional curvature in the Euclidean n-space R-n. In dimension n = 3, this classification was solved by Hasanis and Lopez (2021) [18]. When n > 3, we prove that the separable hypersurfaces of null sectional curvature are three particular families of such hypersurfaces. Finally, we prove that hyperspheres are the only separable hypersurfaces with nonzero constant sectional curvature. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.