免费的CR发行版
Free CR distributions
摘要：
只有一些例外的CR维数和余维数，使几何享受离散分类的逐点类型的齐次模型。CR维数$n$和余维数$n^2$是所谓抛物几何的极少数可能性之一。实际上，齐次模型是具有适当抛物子群$P$的$\PSU(n+1,n)/P$。我们研究了$\mathbb C^{n+n^2}$中这类实$(2n+n^2)$ -维子流形的几何性质，对所有的$n>1$ .特别是，我们表明，基本不变量是扭转型，我们提供了明确的计算，我们讨论了一个类比的February man建设一个圆丛的超曲面型CR几何。
英文摘要：
There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions $n$ and codimensions $n^2$ are among the very few possibilities of the so called parabolic geometries. Indeed, the homogeneous model turns out to be $\PSU(n+1,n)/P$ with a suitable parabolic subgroup $P$. We study the geometric properties of such real $(2n+n^2)$-dimensional submanifolds in $\mathbb C^{n+n^2}$ for all $n>1$. In particular we show that the fundamental invariant is of torsion type, we provide its explicit computation, and we discuss an analogy to the Fefferman construction of a circle bundle in the hypersurface type CR geometry.
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