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, Ann. Math. (2) 72, 445-457 (1960). ZBL0196.54204.)
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.