| In this thesis, isoparametric hypersurfaces of typeⅢin the Lorentzian Space S1n+1 and S15 are studied. It has proved that the typeⅢLorentzian isoparametric hypersurface has at most two different principal curvature .Analytic expressions and local rigidity theorems for Lorentzian isoparametric hypersurface of typeⅢin S15 are given.The paper is organized as follows. In section 1, the historic background of the involved problem is presented and the main results are introduced. In section 2, Lorentzian isoparametric hypersurfaces of typeⅢin S1n+1 is studied. It is proved that the typeⅢLorentzian isoparametric hypersurface has at most two different principal curvature. In section 3, Lorentzian isoparametric hypersurfaces of typeⅢin S15 is studied. It is proved that any Lorentzian isoparametric hypersurface M of typeⅢin S15 is locally congruent to a parallel hypersurface of a Lorentzian isoparametric hypersurface (?) with minimal polynomialλ3. And (?) is determined uniquely by four functions C1(t) ,C2(t) ,C3(t)and C4(t). For Lorentzian isoparametric hypersurface (?) with minimal polynomialλ3 in S15 the analytic expression is given.
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