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arXiv · 2309.06025

Classification of separable hypersurfaces with constant sectional curvature

Muhittin Evren Aydin·Rafael Lopez·Gabriel-Eduard Vilcu
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Abstract

In this paper, we give a full classification of the separable hypersurfaces of constant sectional curvature in the Euclidean $n$-space $\mathbb{R}^n$. In dimension $n=3$, this classification was solved by Hasanis and López [Manuscripta Math. 166, 403-417 (2021)]. 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.

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Muhittin Evren Aydin, Rafael Lopez, Gabriel-Eduard Vilcu. 2023-09-12. Classification of separable hypersurfaces with constant sectional curvature. https://arxiv.org/abs/2309.06025

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