论文摘要
本文通过对三维Lorentz 空间R13、S13、H13中的全脐曲面进行分类,再将R13、S13、H13嵌入到它们的共形紧致化空间Q3.进一步对Q3中的全脐曲面进行分类,并研究这些曲面在嵌入映射下的对应关系,最后对Q3。中的孤立脐点的性质进行研究,得出Q3。中可定向正定闭曲面的脐点指标和定理.全文共分五节. 第一节为引言,第二节介绍R13、S13、H13的共形群,第三节介绍R13、S13、H13中的全脐曲面,第四节介绍Q3中的全脐曲面以及与R13、S13、H13中的全脐曲面的对应关系,第五节介绍Q3。中的脐点指标. 本文通过在Q3上做几何,找出其上的共形不变量以及不变性质,从而得到R13、S13、H13上的某些共形不变性质,而且通过对常曲率分别为0,1,-1的三维Lorentz空间形式R13、S13、H13的共形不变量和不变性质的研究,进而对对了解一般的三维常曲率.Lorentz空间中的某些性质.
论文目录
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