Isoparametric hypersurfaces in product spaces

TL;DR

This paper classifies isoparametric hypersurfaces with constant principal curvatures in product spaces formed by two different constant curvature surfaces, expanding understanding of their geometric properties.

Contribution

It provides a complete characterization and classification of such hypersurfaces in product spaces with distinct constant curvatures.

Findings

Classification of isoparametric hypersurfaces in these product spaces

Explicit descriptions of hypersurfaces with constant principal curvatures

Extension of known results to non-equal curvature product spaces

Abstract

In this paper, we characterize and classify the isoparametric hypersurfaces with constant principal curvatures in the product spaces $ \mathbb{Q}^{2}_{c_{1}} \times \mathbb{Q}^{2}_{c_{2}}$, where $\mathbb{Q}^{2}_{c_{i}}$ is a space form with constant sectional curvature $c_{i}$, for $c_1 \neq c_2$.