关于平面支撑叶理的开3-流形的注记
A note on open 3-manifolds supporting foliations by planes
摘要：
本文证明了：如果开连通的$n$ -流形$N$是由闭平面剖分的$C^{2}$，则$π_{1}(N)$是自由群.这意味着如果$π_{1}(N)$有一个秩大于1的阿贝尔子群，则$\mathcal{F}$至少有一个非闭叶。其次，我们证明了，如果$N$是三维的基本群阿贝尔秩大于1，那么$N$是同胚$\mathbb{T}^2\times \mathbb{R}.$此外，在这种情况下，我们给一个完整的描述的叶理。
英文摘要：
We show that if $N$, an open connected $n$-manifold with finitely generated fundamental group, is $C^{2}$ foliated by closed planes, then $π_{1}(N)$ is a free group. This implies that if $π_{1}(N)$ has an Abelian subgroup of rank greater than one, then $\mathcal{F}$ has at least a non closed leaf. Next, we show that if $N$ is three dimensional with fundamental group abelian of rank greater than one, then $N$ is homeomorphic to $\mathbb{T}^2\times \mathbb{R}.$ Furthermore, in this case we give a complete description of the foliation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
