Isoparametric Hypersurfaces In Lorentz Space Forms

The thesis is mainly to study some isoparametric hypersurfaces with three princi-pal curvatures.In the first part, the thesis introduces the background and development of the isoparametric hypersurfaces.In the second part, the thesis introduces the basic knowledge of the tensor bundle.In the third part, the thesis introduces the basic knowledge of the submanifolds.In the fourth part, the thesis introduces the basic knowledge of the conformal geometry in Lorentz inner product space forms.In the fifth part, the thesis introduces the basic knowledge of the algebra lemma about self-conjugate linear operater.In the sixth part, the thesis introduces the basic knowledge of the completely integrable theorem.The seventh part is the main content of this paper. We will study the isoparametric hypersurfaces with one principal curvature and two principal curvatures.And we will prove our result is unique by complete integrablity.