论文标题
$ \ mathbb c^3 $中的全态性均质真实的超曲面
Holomorphically Homogeneous Real Hypersurfaces in $\mathbb C^3$
论文作者
论文摘要
我们在$ \ mathbb c^3 $中对本地均匀的真实Hypersurfaces进行了完整的描述和分类。在过去的25年中，各种数学家一直在研究这个问题，并且已经研究和分类了几类正在考虑的高空。本文提出的分类问题的最终结果是通过使用抽象5维真实代数的分类获得的，并通过在复杂的3空间中通过霍明态载体场代数来研究其表示。我们获得的成对不等性超曲面的完整列表包含47种类型的同质性超曲面；其中一些类型是1或2-参数家族，而另一些类型是单一的超表面或有限的Hypersurface家族。
We give a complete description and classification of locally homogeneous real hypersurfaces in $\mathbb C^3$. Various groups of mathematicians have been studying this problem in the last 25 years, and several significant classes of hypersurfaces under consideration have been studied and classified. The final results in the classification problem presented in this paper are obtained by using the classification of abstract 5-dimensional real Lie algebras, and by studying their representations by algebras of holomorphic vector fields in complex 3-space. The complete list of pairwise inequivalent hypersurfaces that we obtain contains 47 types of homogeneous hypersurfaces; some of the types are 1- or 2-parametric families, and each of the others is single hypersurface or a finite family of hypersurface.
