Space-like Isoparametric Hypersurfaces in Lorentzian Space Forms

Abstract

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 Hⁿ⁺¹₁ with more than two distinct principal curvatures. It is proved that a space-like isoparametric hypersurface in Hⁿ⁺¹₁ or testSⁿ⁺¹₁ can have at most two distinct principal curvatures. The authors present the classification and explicit analytic expressions of such type of isoparametric hypersurfaces.