In 1960, R. Hermann showed the following:


**Theorem** Let $M$ be a manifold with a foliation $F$ and a bundle-like metric, if all leaves are compact and the holonomy group of each leaf is trivial, then $M/F$ is a smooth manifold. 
(It is the partially result of the main theorem on *Hermann, R.*, [**On the differential geometry of foliations**](http://dx.doi.org/10.2307/1970226), Ann. Math. (2) 72, 445-457 (1960). [ZBL0196.54204](https://zbmath.org/?q=an:0196.54204).)


**Q** If we drop the condition on bundle-like and admit the trivial holonomy group, can we get the same result? That is to say: 


Let $M$ be a manifold with a foliation $F$, if all leaves are compact and diffeomorphism to each other, and the holonomy group of each leaf is trivial, is it true that $M/F$ is a smooth manifold? Any reference is welcome. 



Foliation with trivial leaf holonomy
This follows from Theorem 2 in Thurston's 1974 paper "A generalization of the Reeb stability theorem", at least if $H^1(L,R)=0$.


<https://core.ac.uk/download/pdf/82172971.pdf>


