Isoparametric hypersurfaces in 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 $c_1 \neq c_2$.