论文标题
彩色货架连锁店的谎言理论结构
A Lie-theoretic Construction of Cartan-Moser Chains
论文作者
论文摘要
令$ m^3 \ subset \ mathbb {c}^2 $为$ \ mathcal {c}^ω$ levi nondegenate hypersurface。在文献中，从相当先进的考虑因素中检测到纸箱式连锁店：要么是通过与CR等价问题相关的cartan连接的构建；或构建正式或融合的Poincaré-Moser正常形式。 根据对CR-Transversal曲线的二阶射流空间的检查，本说明提供了一种替代性直接基本结构，该详细延长了$ 5 $无限的全体形态自动形态。在$ 4 $维的喷气纤维中，这些$ 5 $延长的轨道的轨道恰好具有简单的$ 2 $ 2 $二维的变性异常轨道，链基因座：\ [σ_0\，：= \，：= \，\ big \ \ \ {（x_1，y_1，y_1，y_1，y_1，y_1，y_1，x_2，y___2，y__2） \ colon \，\，x_2 = -2x_1^2y_1-2y_1^3，\，\，\，\，\，\，\，\ 2 = 2x_1y_1^2 + 2x_1^3 \ big \}。 \]通过简单的翻译，我们可以仅在概念上的启发下仅在某个点工作，虽然来源和计算都变得令人失望的简单来捕获所有要点。
Let $M^3 \subset \mathbb{C}^2$ be a $\mathcal{C}^ω$ Levi nondegenerate hypersurface. In the literature, Cartan-Moser chains are detected from rather advanced considerations: either from the construction of a Cartan connection associated with the CR equivalence problem; or from the construction of a formal or converging Poincaré-Moser normal form. This note provides an alternative direct elementary construction, based on the inspection of the Lie prolongations of $5$ infinitesimal holomorphic automorphisms to the space of second order jets of CR-transversal curves. Within the $4$-dimensional jet fiber, the orbits of these $5$ prolonged fields happen to have a simple cubic $2$-dimensional degenerate exceptional orbit, the chain locus: \[ Σ_0 \,:=\, \big\{ (x_1,y_1,x_2,y_2) \in \mathbb{R}^4 \colon\,\, x_2 = -2x_1^2y_1-2y_1^3,\,\,\, y_2 = 2x_1y_1^2 + 2x_1^3 \big\}. \] By plain translations, we may capture all points by working only at one point, the origin, and computations, although conceptually enlightening, become disappointingly simple.
