On the existence of exceptional leaves in foliations of co-dimension one
On the existence of exceptional leaves in foliations of co-dimension one
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论同维一叶中特殊叶子的存在
DOI：
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发表时间：
1964
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影响因子：
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通讯作者：
R. Sacksteder
中科院分区：
文献类型：
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作者：
R. Sacksteder
设M是具有余维为1的叶状结构的紧致n-流形（nj> 2）.这样一个叶理的叶称为例外的，如果它在M中无处稠密，但它作为M的子集的拓扑与它作为（n-1）-流形的拓扑不同。Reeb [2]曾问过例外叶是否可能存在于足够光滑的叶理中，他在[2]中证明，在某些条件下，例外叶不存在。作者在文[3]和[4]中证明了这类定理。在这里，我们将回答里布的问题，给出一个例子，3流形的C叶状结构的余维1，其中有例外的叶子。此外，这些叶子将包含在一个最小的叶理集。
Let M be a compact n-manifold {n j> 2) with a foliated structure of co-dimension one. A leaf of such a foliation is said to be exceptional if it is nowhere dense in M, but its topology as a subset of M is not the same as its topology as an (n-1)-manifold. Reeb [2] has asked if it is possible for exceptional leaves to exist in sufficiently smooth foliations, and he showed in [2] that, under certain conditions, exceptional leaves do not exist. The author proved other theorems of this type in [3] and [4]. Here we shall answer Reeb's question by giving an example of a 3-manifold with a C foliated structure of co-dimension one in which there are exceptional leaves. Moreover, these leaves will be contained in a minimal set of the foliation.