Isoparametric hypersurfaces in product spaces

In this paper, we characterize and classify the isoparametric hypersurfaces with constant principal curvatures in the product spaces ${\mathbb{Q}}_{c_1}^2\times {\mathbb{Q}}_{c_2}^2$, where ${\mathbb{Q}}_{c_i}^2$ is a space form with constant sectional curvature $c_i$, for $c_1\mathrm{\ne }{c}_2$.