Singular Riemannian Foliations
Singular Riemannian Foliations
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奇异黎曼叶状结构
DOI：
10.1007/978-1-4684-8670-4_6
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发表时间：
1988
影响因子：
1.8
通讯作者：
P. Molino
中科院分区：
文献类型：
--
作者：
P. Molino
我们在上一章描述的黎曼叶理的整体几何，自然地引导我们考虑“奇异”黎曼叶理。事实上，如果（M，F，g T）是紧致连通流形上的黎曼叶化，则M被叶闭包的划分\（\overline F\）在奇异闭包之外定义了黎曼叶化。此外，横向的叶，这个分区是局部定义的轨道的李代数的Killing向量场。这是奇异黎曼叶理的一个典型例子。
The global geometry of Riemannian foliations that we depicted in the last chapter leads us naturally to consider “singular” Riemannian foliations. Indeed, if (M, F, g T ) is a Riemannian foliation on a compact connected manifold, then the partition \(\overline F\) of M by the leaf closures defines, outside the singular closures, a Riemannian foliation. Moreover, transverse to the leaves, this partition is locally defined by the orbits of a Lie algebra of Killing vector fields. This is a typical example of a singular Riemannian foliation.