4维洛伦兹中的洛伦兹等参超曲面

4-D Lorentzian Isoparametric Hypersurfaces in Lorentzian Speres

研究了S1^4（4维洛伦兹球面）中的Ⅲ型洛伦兹等参超曲面。说明了S1^4中的任何Ⅲ型洛伦兹等参超曲面M局部地与最小多项式为λ^3的某个洛伦兹等参超曲面^～M的平行超曲面叠合,还证明了这种超曲面^～M局地被三个一元函数C1（u）,C2（u）,C3（u）所唯一确定,并给出了^～M的解析表达式。从而完成了S1^4中洛伦兹等参超曲面的完全分类。

In the present paper isoparametric hypersurfaces in the Lorentzian sphere S1^4 are studied. It is proved that any Lorentzian isoparametric hypersurface M of type Ⅲ in S1^4 is locally congruent to a parallel hypersurface of a Lorentzian isoparametric hypersurface ^~M with minimal polynomial λ^3. And ^~M is determined uniquely by three functions C1 （u） , C2 （u） and C3 （u）. For Lorentzian isoparametric hypersurface ^~M with minimal polynomial λ^3 in S1^4 the analytic expression is given. This together with former papers of other authors completes the classification of Lorentzian isoparametric hypersurfaces in S1^4.