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Homogeneous Surfaces in $$\mathbb C^4$$ Associated with a 5-Dimensional Completely Nondegenerate Cubic Model Surface of CR-Type $$(1,3)$$
Russian Journal of Mathematical Physics ( IF 1.4 ) Pub Date : 2020-12-22 , DOI: 10.1134/s1061920820040020
V. K. Beloshapka , M. Sabzevari

Abstract

The action on the space \(\mathbb C^4\) of the 7-dimensional Lie group of infinitesimal holomorphic automorphisms of a completely nondegenerate cubic model surface \(Q\) of CR-type \((1,3)\) is considered. All orbits of the given action are found and their biholomorphic classification is given. One of the orbits coincides with the surface \(Q\) (the 5-dimensional orbit), two orbits are 6-dimensional, and the remaining part of the space \(\mathbb C^4\), the complement to the above orbits, foliates into 7-dimensional real orbits. It is also proved that the algebra of infinitesimal holomorphic automorphisms of all orbits, except for the twelve holomorphically degenerate orbits, coincides with the algebra of the surface \(Q\).



中文翻译:

$$ \ mathbb C ^ 4 $$中的同质曲面与CR型$$(1,3)$$的5维完全非简并三次模型曲面相关联

摘要

对CR型\((1,3)\)的完全非简并三次立方形模型表面\(Q \)的极小全同构同构的7维Lie群的空间\(\ mathbb C ^ 4 \)的作用被认为。找到给定动作的所有轨道,并给出其全同性分类。轨道之一与表面\(Q \)(5维轨道)重合,两个轨道为6维,其余部分为空间((mathbb C ^ 4 \))是上述轨道的补充,形成了7维真实轨道。还证明了除十二个全纯简并轨道之外,所有轨道的无穷小全纯自同构的代数与表面\(Q \)一致

更新日期:2020-12-23
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