Research Of Lorentzian Isoparametric Hypersurfaces Of TypeⅢ In S₁ⁿ⁺¹

For a long time, the isoparametric hypersurface is an important item in geometry. And its classification problem is more important.This paper with the help of moving equation and moving frame study the Lorentzian isoparametric hypersurfaces of Type Ⅲ in the Lorentzian sphere S1(n+1) ((?) R1(n+2). The existence theorem and local rigidity theorem for Lorentzian isoparametric total-umbilical and semi-umbilical hypersurfaces of type Ⅲ in S1(n+1) and its classification are given.This paper’s structure is as follows:In chapter 1, the historic background of the involved problem is presented and the main results are stated.In chapter 2, we will give out basic formulae of total-umbilical lorentzian isoparametric hypersurface of the type Ⅲ in S1(n+1),then choose local coordinate and local frame. This result enable us proof of uniqueness theorem,and the explicit analytic expressions is given.In chapter 3, we will give out basic formulae of semi-umbilical lorentzian isoparametric hypersurface of the type Ⅲ in S1(n+1),then choose local coordinate and local frame. This result enable us proof of uniqueness theorem,and the explicit analytic expressions is given.