Embeddability for three-dimensional CR-manifolds
Embeddability for three-dimensional CR-manifolds
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DOI：
10.1090/s0894-0347-1990-1071115-4
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发表时间：
1990-01
影响因子：
3.9
通讯作者：
D. Burns;C. Epstein
中科院分区：
文献类型：
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作者：
D. Burns;C. Epstein
在紧致三维CR-流形理论中的一个主要兴趣问题是理解当一个给定的严格伪凸的CR-结构可以通过嵌入C'来实现时。我们把这种可能的结构称为可嵌入的，否则称为不可嵌入的。这个问题是唯一感兴趣的三维Boutet德蒙维尔定理指出，任何严格的伪凸CR-结构，在一个紧凑的（2d + 1）-流形，是可实现的嵌入在一些C'，提供d > 1。另一方面，有一个经典的例子罗西这表明，一个任意小，真实的分析，扰动的标准结构上的三个领域可能无法嵌入，[罗斯]。后来，尼伦伯格建造了W？？扰动，其中相关联的奥布方程未能甚至局部解决方案，[N]。事实上，这种情况在F？topology.现在主要从Eliashberg的工作中了解到，
A question of principal interest in the theory of compact, three-dimensional CR-manifolds is to understand when a given strictly pseudoconvex, CR-structure can be realized by an embedding in C' . We call a structure for which this is possible embeddable, and nonembeddable otherwise. This question is only of interest in three dimensions as a theorem of Boutet de Monvel states that any strictly pseudoconvex CR-structure, on a compact (2d + 1)-manifold, is realizable as an embedding in some C' , provided d > 1. On the other hand, there is a classical example of Rossi which shows that an arbitrarily small, real analytic, perturbation of the standard structure on the three sphere may fail to be embeddable, [Ros]. Later, Nirenberg constructed W??-perturbations for which the associated Ob-equation fails to have even local solutions, [N]. In fact, this situation is generic in the F?-topology. It is now understood, principally from the work of Eliashberg, that CR-structures with