Engel流形中切线和横向浸入的灵活性
Flexibility for tangent and transverse immersions in Engel manifolds
摘要：
在这篇文章中，我们研究的浸入的圆是切的恩格尔结构$\mathcal{D}$。我们表明，一个完整的$h$原则确实存在，只要一个排除闭轨道的$\mathcal{W}$，内核的$\mathcal{D}$。这是尖锐的：我们详细阐述了Bryant和Hsu的工作，以表明与$\mathcal{W}$相切的曲线通常符合不能在形式水平上检测到的附加孤立分量。然后，我们表明，这是一个例外的现象：如果$\mathcal{D}$是通用的，曲线相切的$\mathcal{W}$不再孤立。然后，我们继续表明，一个完整的$h$ -原则成立浸泡横向恩格尔结构。
英文摘要：
In this article we study immersions of the circle that are tangent to an Engel structure $\mathcal{D}$. We show that a full $h$-principle does exist as soon as one excludes the closed orbits of $\mathcal{W}$, the kernel of $\mathcal{D}$. This is sharp: we elaborate on work of Bryant and Hsu to show that curves tangent to $\mathcal{W}$ often conform additional isolated components that cannot be detected at a formal level. We then show that this is an exceptional phenomenon: if $\mathcal{D}$ is generic, curves tangent to $\mathcal{W}$ are not isolated anymore. We then go on to show that a full $h$-principle holds for immersions transverse to the Engel structure.
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