论文标题
2-非排效器Cr几何形状的基本不变性与简单模型
Fundamental invariants of 2--nondegenerate CR geometries with simple models
论文作者
论文摘要
本文研究了具有简单模型的2-核代理几何形状的基本不变性。我们表明，这些不变的有两个来源。第一个来源是（局部）在Levi内核的叶片空间上出现的抛物线几何形状的谐波曲率。第二个来源是CR几何形状的复杂切线空间上的复杂结构与与基础抛物线几何的对应空间上的复杂结构之间的差异。我们表明，后来的基本不变性仅在模型是通用的情况下才会出现，如果它们消失了，那么局部对等问题的解决方案是2-非等级CR几何形状具有简单模型，这是由基础抛物线几何学的cartan连接提供的。我们表明，可以作为模型的变形获得具有后来基本不变的Cr几何形状的非平凡示例。
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.
