论文标题
关于$ 2 $ 2 $ nonondementore cr typerface类型和标志结构的几何形状和李维叶叶的标志结构
On geometry of $2$-nondegenerate CR structures of hypersurface type and flag structures on leaf spaces of Levi foliations
论文作者
论文摘要
我们在配备$ 2 $ nondementer的，超出表面的cr cr结构的内分析歧管上构建了规范的绝对平行性，这些任意奇数尺寸不少于$ 7 $，其levi内核具有恒定的等级，属于我们将我们标记为可回收的cr cr结构的恒定等级。为此，我们基于将CR结构相关的Levi叶片的叶片空间上的特殊标志结构减少到特殊的标志结构（称为动力的Legendrian接触结构）的新方法。这将Porter-Zelenko [20]的结果从构成所有CR符号集中的离散集的常规CR符号的情况扩展到任意CR符号的情况，可以从其从其相应的动态传说传奇触点结构中独特地恢复原始CR结构。我们的方法阐明了Porter-Zelenko [20]中开发的常规符号的大田中延长与他们通常的田中延长之间的关系，从而提供了对它们相等的条件的几何解释。通过寻找具有给定非规范符号的均质模型的搜索，我们还描述了从原始的自然框架捆绑包中减少的过程，这对于具有不规则CR符号的结构是不可避免的。我们为示例提供了这种减少程序，其基础歧管具有$ 7 $和$ 9 $的尺寸。我们表明，对于任何固定等级$ r> 1 $，在与2-二键型，高度表面型CR cr歧管相关的所有CR符号中，其奇数大于$ 4R+1 $的cr歧管与等级$ r $ r $ r $ r $ levi kernel相关，cr符号与任何同质模型无关，对于$ r = 1 $，如果是cr = 1 $，则相同的结果是pee is pece。
We construct canonical absolute parallelisms over real-analytic manifolds equipped with $2$-nondegenerate, hypersurface-type CR structures of arbitrary odd dimension not less than $7$ whose Levi kernel has constant rank belonging to a broad subclass of CR structures that we label as recoverable. For this we develop a new approach based on a reduction to a special flag structure, called the dynamical Legendrian contact structure, on the leaf space of the CR structure's associated Levi foliation. This extends the results of Porter-Zelenko [20] from the case of regular CR symbols constituting a discrete set in the set of all CR symbols to the case of the arbitrary CR symbols for which the original CR structure can be uniquely recovered from its corresponding dynamical Legendrian contact structure. Our method clarifies the relationship between the bigraded Tanaka prolongation of regular symbols developed in Porter-Zelenko [20] and their usual Tanaka prolongation, providing a geometric interpretation of conditions under which they are equal. Motivated by the search for homogeneous models with given nonregular symbol, we also describe a process of reduction from the original natural frame bundle, which is inevitable for structures with nonregular CR symbols. We demonstrate this reduction procedure for examples whose underlying manifolds have dimension $7$ and $9$. We show that, for any fixed rank $r>1$, in the set of all CR symbols associated with 2-nondegenerate, hypersurface-type CR manifolds of odd dimension greater than $4r+1$ with rank $r$ Levi kernel, the CR symbols not associated with any homogeneous model are generic, and, for $r=1$, the same result holds if the CR structure is pseudoconvex.
