C^4中五维完全非退化CR流形的收敛正规形
复变函数
2020-05-08 v2 微分几何
摘要
应用等变活动标架法，我们为C^4中实解析的五维完全非退化CR子流形构造了收敛正规形。这些CR流形被划分为若干双全纯不等价的子类，每一子类都有其自身的完全正规形。此外，我们证明了在双全纯意义下，Beloshapka三次模型是该类流形中对应无穷小CR自同构代数维数达到最大可能值七的唯一成员。我们的结果亦有助于研究CR流形之间的双全纯等价问题。
引用
@article{arxiv.2004.11251,
title = {Convergent normal forms for five dimensional totally nondegenerate CR manifolds in C^4},
author = {Masoud Sabzevari},
journal= {arXiv preprint arXiv:2004.11251},
year = {2020}
}
备注
As kindly noticed by Maria Stepanova, a computational error is found in the first version of the paper, concerning the computations of Branch 3-3-1 (Section 7.2.1). This error is corrected and the presentation is modified