  We show that if $N$, an open connected $n$-manifold with finitely generated
fundamental group, is $C^{2}$ foliated by closed planes, then $\pi_{1}(N)$ is a
free group. This implies that if $\pi_{1}(N)$ has an Abelian subgroup of rank
greater than one, then $\mathcal{F}$ has at least a non closed leaf. Next, we
show that if $N$ is three dimensional with fundamental group abelian of rank
greater than one, then $N$ is homeomorphic to $\mathbb{T}^2\times \mathbb{R}.$
Furthermore, in this case we give a complete description of the foliation.
