Geodesic
A test for compactness of a foliation
Matematičeskie zametki, Tome 58 (1995) no. 6, pp. 872-877 
I. A. Melnikova. A test for compactness of a foliation. Matematičeskie zametki, Tome 58 (1995) no. 6, pp. 872-877. http://geodesic.mathdoc.fr/item/MZM_1995_58_6_a6/
@article{MZM_1995_58_6_a6,
     author = {I. A. Melnikova},
     title = {A~test for compactness of a~foliation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {872--877},
     year = {1995},
     volume = {58},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_6_a6/}
}
TY  - JOUR
AU  - I. A. Melnikova
TI  - A test for compactness of a foliation
JO  - Matematičeskie zametki
PY  - 1995
SP  - 872
EP  - 877
VL  - 58
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_1995_58_6_a6/
LA  - ru
ID  - MZM_1995_58_6_a6
ER  - 
%0 Journal Article
%A I. A. Melnikova
%T A test for compactness of a foliation
%J Matematičeskie zametki
%D 1995
%P 872-877
%V 58
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1995_58_6_a6/
%G ru
%F MZM_1995_58_6_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate foliations on smooth manifolds that are determined by a closed 1-form with Morse singularities. We introduce the notion of the degree of compactness and prove a test for compactness.

[1] Novikov S. P., “Gamiltonov formalizm i mnogoznachnyi analog teorii Morsa”, UMN, 37:5 (1982), 3–49 | MR | Zbl

[2] Novikov S. P., “Kriticheskie tochki i poverkhnosti urovnya mnogoznachnykh funktsii”, Tr. MIAN, 166, Nauka, M., 1984, 201–209 | MR | Zbl

[3] Zorich A. V., “Kvaziperiodicheskaya struktura poverkhnostei urovnya morsovskoi 1-formy, blizkoi k ratsionalnoi, – zadacha S. P. Novikova”, Izv. AN SSSR. Ser. matem., 51:6 (1987), 1322–1344 | Zbl

[4] Le T. K. T., “Struktura poverkhnostei urovnya morsovskoi formy”, Matem. zametki, 44:1 (1988), 124–133 | MR

[5] Alaniya L. A., “O topologicheskoi strukture poverkhnostei urovnya morsovskikh 1-form”, UMN, 46:3 (1991), 179–180 | MR

[6] Melnikova I. A., “Priznak nekompaktnosti sloeniya na $M_g^2$”, Matem. zametki, 53:3 (1993), 158–160 | MR | Zbl

[7] Henc Damir, “Ergodicity of foliations with singularities”, J. Func. Anal., 75:2 (1987) | MR | Zbl

[8] Dold A., Lektsii po algebraicheskoi topologii, Mir, M., 1976