Abstract：In the present paper the Lorentzian isoparametric hypersurfaces M of type Ⅱ in the Lorentzian sphere S1n+1 are studied.The existence theorem and local rigidity theorem for those hypersurfaces are given.The hypersurface M is totally umbilical if all the principal curvatures of M equal to each other.Suppose M has two distinct principal curvatures a1,an(a1≠an) and the minima polynomial of the shape operator A of M is(λ-a1)2(λ-an).The hypersurface M is semi-umbilical if the multiplicity of a1 is p=2.It is proved that M can be obtained by parallel translation of product S+p-1(t)×Sn-p(t) of two manifolds along each line Lt in a family {Lt|t∈I} of 1-parameter light-like lines.Particularly M is totally umbilical if p=n,and M is semi-umbilical if p=2.
2012, Vol. 36 
