Questions tagged [foliations]

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80 questions
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What meaning of this sentence?

I study about Poisson geometry. You should be know that every Poisson structure induced singular foliation. I encountered this sentence “Two points lie in the same leaf if and only if one is ...
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Phase, Isochrons, Isochrons map and Lift

at the moment i read the following paper: https://arxiv.org/pdf/1512.04436v1.pdf I have some questions about it and i hope someone can help me. On page 4/5 they introduce isochrons and the isochron ...
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Lie group action and foliation

Let $M$ be a smooth manifold, and $G$ be a compact Lie group acting on $M$ smoothly. We assume that isotropic group of any point $x\in M$ is of dimension zero. Q How to show that $M$ admits a ...
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Integrability of distributions which are invariant under isometry group

Let $(M.g)$ be a Riemannian manifold and $D$ is a distribution on $M$. Assume that $D$ is invariant under the action of the isometry group of $M$. Under which conditions such $D$ ...
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Foliations vs Laminations

What's the big difference/similarity between foliations and laminations? What kind of theorems hold for both of them? Is there something that makes them essentially the same/different?
If I have $u:M\rightarrow D\setminus 0$, $M\subseteq (\mathbb C^2,0)$ compact, $\mathbb C^2 = \mathbb C \times \mathbb C$ and $D$ the Poincare disk, $u$ is holomorphic, surjective, proper and every ...
I have been told the following fact: Given a foliation $F$ of a smooth manifold $M$, then the projection $\pi : M \to M /F$ onto the space of leaves (points on the same leaf are identified) is open. ...