Isoparametric hypersurfaces in product spaces of space forms

Abstract

We give a complete classification of isoparametric hypersurfaces in a product space Mκ12×Mκ22 of 2-dimensional space forms for κi∈{−1,0,1} with κ1≠κ2. In fact we prove that any isoparametric hypersurface in such a space has constant product angle function, which enables us to remove the condition of constant principal curvatures from the classification obtained recently by J.B.M. dos Santos and J.P. dos Santos.