SMOOTHNESS OF ISOMETRIC FLOWS ON ORBIT SPACES AND APPLICATIONS
SMOOTHNESS OF ISOMETRIC FLOWS ON ORBIT SPACES AND APPLICATIONS
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轨道空间等距流动的光滑性及应用
DOI：
10.1007/s00031-016-9386-5
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发表时间：
2013
影响因子：
0.7
通讯作者：
M. Radeschi
中科院分区：
文献类型：
--
作者：
Marcos M. Alexandrino;M. Radeschi
本文证明了：给定完备黎曼流形M上的一个适当的等距作用K × M → M，则轨道空间M/K上的每个连续等距流都是光滑的，即，它是K-等变光滑流在流形M上的投影。作为一个直接推论，我们推出轨道空间上等距作用的光滑性。我们的结果的另一个相关应用涉及莫利诺猜想，它指出，一个黎曼流形的分区到一个奇异黎曼叶状的叶子的闭包仍然是一个奇异黎曼叶状。我们证明莫利诺猜想的主要类叶理考虑在他的书中，即轨道状叶理。
We prove here that given a proper isometric action K × M → M on a complete Riemannian manifold M, then every continuous isometric flow on the orbit space M/K is smooth, i.e., it is the projection of a K-equivariant smooth flow on the manifold M. As a direct corollary we infer the smoothness of isometric actions on orbit spaces. Another relevant application of our result concerns Molino’s conjecture, which states that the partition of a Riemannian manifold into the closures of the leaves of a singular Riemannian foliation is still a singular Riemannian foliation. We prove Molino’s conjecture for the main class of foliations considered in his book, namely orbit-like foliations.