Codimension one foliations of flat 3-manifolds

In this paper we study $C^r$ ($r\geqslant 2$) codimension one foliations of closed 3-manifolds. We describe all closed flat 3-manifolds that admit foliations without compact leaves, and all closed flat 3-manifolds on which every $C^r$ ($r\geqslant 2$) codimension one foliation has a compact leaf and this leaf is either a 2-torus or a Klein bottle.