Geodesic
Codimension one foliations of flat 3-manifolds
Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 823-833

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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. 
@article{SM_1996_187_6_a2,
     author = {V. K. Mamaev},
     title = {Codimension one foliations of flat 3-manifolds},
     journal = {Sbornik. Mathematics},
     pages = {823--833},
     publisher = {mathdoc},
     volume = {187},
     number = {6},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_6_a2/}
}
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V. K. Mamaev. Codimension one foliations of flat 3-manifolds. Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 823-833. http://geodesic.mathdoc.fr/item/SM_1996_187_6_a2/