Geodesic
Codimension one foliations of flat 3-manifolds
Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 823-833 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {1996},
     volume = {187},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_6_a2/}
}
TY  - JOUR
AU  - V. K. Mamaev
TI  - Codimension one foliations of flat 3-manifolds
JO  - Sbornik. Mathematics
PY  - 1996
SP  - 823
EP  - 833
VL  - 187
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/SM_1996_187_6_a2/
LA  - en
ID  - SM_1996_187_6_a2
ER  - 
%0 Journal Article
%A V. K. Mamaev
%T Codimension one foliations of flat 3-manifolds
%J Sbornik. Mathematics
%D 1996
%P 823-833
%V 187
%N 6
%U http://geodesic.mathdoc.fr/item/SM_1996_187_6_a2/
%G en
%F SM_1996_187_6_a2
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/

[1] Aranson S. Kh., “Traektorii na neorientiruemykh dvumernykh mnogoobraziyakh”, Matem. sb., 80 (122):3 (1969), 314–333 | MR | Zbl

[2] Aranson S. Kh., Zhuzhoma E. V., “O topologicheskoi klassifikatsii sloenii Riba korazmernosti odin na trekhmernom tore”, Metody kachestvennoi teorii differentsialnykh uravnenii, Mezhvuz. tematich. sb. nauchn. tr., ed. E. A. Leontovich-Andronova, Gork. gos. un-t, Gorkii, 1978, 41–64 | Zbl

[3] Volf Dzh., Prostranstva postoyannoi krivizny, Nauka, M., 1982 | MR

[4] Lokot T. V., Klassy vrascheniya dlya sloenii korazmernosti odin s trivialnymi gruppami golonomii i ikh primeneniya, Diss. ...kand. fiz.-matem. nauk, MGU, M., 1972

[5] Matveev S. V., Chernavskii A. V., Osnovy topologii mnogoobrazii, Krasnodar, 1974 | MR

[6] Novikov S. P., “Topologiya sloenii”, Tr. MMO, 14, URSS, M., 1965, 248–278 | MR | Zbl

[7] Solodov V. V., “Gomeomorfizm pryamoi i sloeniya”, Izv. AN SSSR. Ser. matem., 46:5 (1982), 1047–1061 | MR | Zbl

[8] Solodov V. V., “Gomeomorfizmy okruzhnosti i sloeniya”, Izv. AN SSSR. Ser. matem., 48:3 (1984), 599–613 | MR | Zbl

[9] Tamura I., Topologiya sloenii, Mir, M., 1979 | MR | Zbl

[10] Baer R., “Isotopie von Kurven auf orientierbaren geschlossenen Flächen und ihr Zusammenhang mit topologischen Deformation der Flächen”, J. Reine Angew. Math., 159:2 (1928), 101–116 | Zbl

[11] Haefliger A., “Variétés feuilletées”, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 16:3 (1962), 367–397 | MR | Zbl

[12] Imanishi H., “On the theorem of Denjoy–Sacksteder for codimension one foliations without holonomy”, J. Math. Kyoto Univ., 14:3 (1974), 607–634 | MR | Zbl

[13] Kneser H., “Reguläre Kurvenscharen auf Ringflächen”, Math. Ann., 91 (1924), 135–154 | DOI | MR | Zbl

[14] Lamoureux C., “Quelques conditions d'existence de feuilles compactes”, Ann. Inst. Fourier (Grenoble), 24:4 (1974), 229–240 | MR | Zbl

[15] Markley N. G., “The Poincare–Bendixon theorem for the Klein bottle”, Trans. Amer. Math. Soc., 135 (1969), 159–165 | DOI | MR | Zbl

[16] Moussu R., “Feuilletage sans holonomie d'une variété fermée”, C. R. Acad. Sci. Paris Sér. I Math., 270:20 (1970), A1308–A1311 | MR

[17] Moussu R., Roussarie R., “Une condition suffisante pour qu'un feuilletage soit sans holonomie”, C. R. Acad. Sci. Paris Sér. I Math., 271:4 (1970), A240–A243 | MR

[18] Plante J., “Foliations with measure preserving holonomy”, Ann. of Math., 102:2 (1975), 327–361 | DOI | MR | Zbl

[19] Rosenberg H., “Foliations by planes”, Topology, 1968, no. 7, 131–138 | DOI | MR | Zbl

[20] Schweitzer P., “Compact leaves of codimension one foliations”, Lecture Notes in Math., 484, 1975, 273–276 | MR | Zbl

[21] Wood J., “Foliations on $3$-manifolds”, Ann. of Math., 89:2 (1970), 336–358 | DOI | MR