Are there examples of codimension 2 foliations on simply connected compact 4-manifolds such that
- Every leaf is diffeomorphic to $\mathbb R^2$
- Every leaf is dense?
Same question for 5-manifolds and foliations of with leaves diffeomorphic to $\mathbb R^2$ or $\mathbb R^3$.
I am trying to show absence of Anosov diffeos on simply connected 4 and 5 manifolds and I would like to make sure I am not missing any important foliation theory background. So relevant references will be very much appreciated.