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. This paper was translated from J. Nanchang Univ. Nat. Sci. Ed., 2004, 28(2): 113–117