Hypersurfaces with constant sectional curvature of $\Sf^n\times \R$ and $\Hy^n\times \R$

TL;DR

This paper classifies hypersurfaces with constant sectional curvature in the product spaces ^n  ^n imes \u211d and ^n ^n imes ^n for dimensions n  3, providing a comprehensive understanding of their geometric structure.

Contribution

It provides a complete classification of hypersurfaces with constant sectional curvature in these specific product spaces, extending previous geometric results.

Findings

Classification of hypersurfaces with constant sectional curvature in ^n  ^n imes ^n and ^n ^n imes ^n

Identification of geometric properties unique to these hypersurfaces

Extension of known results to higher dimensions n  3

Abstract

We classify the hypersurfaces of $\Sf^n\times \R$ and $\Hy^n\times \R$ with constant sectional curvature and dimension $n\geq 3$.