Space-like isoparametric hypersurfaces in Lorentzian space forms

The purpose of this paper is to make clear the so-called Nomizu problem, whether it is possible to find examples of space-like isoparametric hypersurfaces in H 1 n+1 with more than two distinct principal curvatures. It is proved that a space-like isoparametric hypersurface in H 1 n+1 or S 1 n+1 can have at most two distinct principal curvatures. The authors present the classification and explicit analytic expressions of such type of isoparametric hypersurfaces. © Higher Education Press and Springer-Verlag 2006.