Fundamental invariants of 2--nondegenerate CR geometries with simple models.
Fundamental invariants of 2--nondegenerate CR geometries with simple models.
复制标题
2-非简并 CR 几何的基本不变量与简单模型。
DOI：
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发表时间：
2020
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通讯作者：
Jan Gregorovivc
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作者：
Jan Gregorovivc
本文研究了具有简单模型的2—非退化CR几何的基本不变量。我们证明了这些不变量有两个来源。第一个来源是（局部）出现在Levi核叶空间上的抛物几何的调和曲率。第二个来源是CR几何的复切线空间上的复杂结构与底层抛物线几何对应空间上的复杂结构之间的差异。我们证明了后面的基本不变量只有在模型是一般的情况下才会出现，如果它们消失，则利用底层抛物几何的Cartan连接提供了具有简单模型的2—非退化CR几何的局部等价问题的解。我们证明了具有后期基本不变量的CR几何的非平凡例子可以作为模型的变形而得到。
This article studies the fundamental invariants of 2--nondegenerate CR geometries with simple models. We show that there are two sources of these invariants. The first source is the harmonic curvature of the parabolic geometry that appears (locally) on the leaf space of the Levi kernel. The second source is the difference between the complex structure on the complex tangent space of the CR geometry and the complex structure on the correspondence space to the underlying parabolic geometry. We show that the later fundamental invariants appear only when the model is generic and if they vanish, then the solution of the local equivalence problem of 2--nondegenerate CR geometries with simple models is provided by the Cartan connection of the underlying parabolic geometry. We show that nontrivial examples of CR geometries with the later fundamental invariants can be obtained as deformations of the models.