On hypersurfaces of ℍ 2 × ℍ 2

In this paper, we study hypersurfaces of ℍ 2 × ℍ 2 . We first classify the hypersurfaces with constant principal curvatures and constant product angle functions. Then we classify homogeneous hypersurfaces and isoparametric hypersurfaces, respectively. Finally, we classify the hypersurfaces with at most two distinct constant principal curvatures, as well as those with three distinct constant principal curvatures under some additional conditions.