论文标题
水平曲线的微叶状和局部可集成性
Microflexiblity and local integrability of horizontal curves
论文作者
论文摘要
令$ξ$为分析括号生成的分布。我们表明，单数的细菌子空间（从控制理论的意义上）在平滑曲线的细菌空间内具有无限的编imension，切成$ξ$。我们将其形式化为关于切线曲线有限喷射的渐近陈述。在分析环境中，这解决了Y. Eliashberg和N.M. Mishachev的猜想，涉及M. Gromov关于切相条件的微遗漏性的较早主张。 从这些陈述中，由于格罗莫夫·格罗莫夫（M.
Let $ξ$ be an analytic bracket-generating distribution. We show that the subspace of germs that are singular (in the sense of Control Theory) has infinite codimension within the space of germs of smooth curves tangent to $ξ$. We formalise this as an asymptotic statement about finite jets of tangent curves. This solves, in the analytic setting, a conjecture of Y. Eliashberg and N.M. Mishachev regarding an earlier claim by M. Gromov about the microflexibility of the tangency condition. From these statements it follows, by an argument due to M. Gromov, that the $h$-principle holds for maps and immersions transverse to $ξ$.
