Total Umbilical And Semi-Umbilical Lorentzian Isoparametric Hypersurfaces Of Type Ⅲ In S₁ⁿ⁺¹

As every knows, isoparametric hypersurfaces is an important item, the more impantant thing is that classify once done, more important cnclution can come into being immediately.This thesis with the help of moving equetion study the Lorentzian isoparametric hypersurfaces of Type Ⅲ in the Lorentzian sphere S1n+1The existence theorem and local rigidity theorem for Lorentzian isoparametric total-umbilical and semi-umbilical hypersurfaces of type Ⅲ in S1n+1and its classification are given.This paper’s structrue is as follows:In section1, the historic background of the involved problem is presented and the main results are stated.In section2.the existence and unicity of classify of the type Ⅲ total-umbilical lorentzian isoparametric hypersurface is studied.In section3.the existence and unicity of classify of the type Ⅲ semi-umbilical lorentzian isoparametric hypersurface is studied.In section4.the existence and unicity of classify of the type Ⅲ non-umbilical lorentzian withωω=0isoparametric hypersurface is studied.