Isoparametric hypersurfaces in products of simply connected space forms

For i∈ \1,2\, i ∈ { 1 , 2 } , let Q ε ᵢnᵢ Q ϵ i n i denote the simply connected space form of dimension nᵢ≥ 2 n i ≥ 2 and constant sectional curvature ε ᵢ∈ R ϵ i ∈ R , (ε ₁,ε ₂)≠ (0,0) ( ϵ 1 , ϵ 2 ) ≠ ( 0 , 0 ) . We prove that any connected isoparametric hypersurface of Q ε ₁n₁× Q ε ₂n₂ Q ϵ 1 n 1 × Q ϵ 2 n 2 has constant angle function. We use this property to classify both the isoparametric and homogeneous hypersurfaces of Q ε ₁n₁× Q ε ₂n₂ Q ϵ 1 n 1 × Q ϵ 2 n 2 when ε ₁ε ₂≤ 0 ϵ 1 ϵ 2 ≤ 0 . Under additional hypotheses, we obtain a similar classification result in the case ε ₁ε ₂> 0 ϵ 1