Those Space-like Hypersurfaces With The Three Conformal Principal Curvature

After classifying those space-like hypersurfaces with two conformal principal curvature in the Lorentz space forms,this paper studies those space-like hypersurfaces with the three conformal principal curvature.The first chapter introduces the research background and research contents.The second chapter introduces the pseudo Riemannian manifolds,and calculates the basic equations in the three types of space forms.The third chapter mainly introduces the basic knowledge of conformal geometry,and presents those conformal invariants in an isometric interpretation.The fourth chapter demonstrates that if a space-like isoparametric hypersurface has three distinct conformal principal curvature of the same multiplicity,then it must be of non-parallel second fundamental form,and we classify this class of hypersurface up to the conformal equivalence.