Lagrangian holonomy ; characteristic elements of a lagrangian foliation
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 1 (2002) no. 2, p. 319-326
Let ℒ be a lagrangian foliation on a symplectic manifold (M 2n ,ω). The characteristic elements of such a foliation associated to a lagrangian total transversal are obtained; they are a generalisation of the characteristic elements given by J.J. Duistermaat [5]. This technique is applied to give a classification of the germs of lagrangian foliation along a compact leaf. Several examples of classification are given.
Classification:  53C12,  58F05 
@article{ASNSP_2002_5_1_2_319_0,
     author = {Curr\'as-Bosch, Carlos and Molino, Pierre},
     title = {Lagrangian holonomy ; characteristic elements of a lagrangian foliation},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {2},
     year = {2002},
     pages = {319-326},
     zbl = {1097.53015},
     mrnumber = {1991142},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2002_5_1_2_319_0}
}

Currás-Bosch, Carlos; Molino, Pierre. Lagrangian holonomy ; characteristic elements of a lagrangian foliation. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 1 (2002) no. 2, pp. 319-326. http://www.numdam.org/item/ASNSP_2002_5_1_2_319_0/

[1] R. Bott, “Lectures on characteristic classes and foliations”, Lecture Notes in Math. 279 (1972). | MR 362335 | Zbl 0241.57010

[2] C. Currás-Bosch - P. Molino, Un exemple de classification de germes de feuilletages Lagrangiens au voisinage d'une feuille compacte, Indag. Math. 9(2) (1998), 197-209. | MR 1691432 | Zbl 0939.53019

[3] C. Currás-Bosch - P. Molino, Holonomie, suspensions et classifications pour les feuilletages Lagrangiens, C.R. Acad. Sci. Paris Sér. I Math. 326(1) (1998), 1317-1320. | MR 1649144 | Zbl 0908.53010

[4] P. Dazord, Sur la géométrie des sous-fibrés et des feuilletages Lagrangiens, Ann. Sci. École Norm. Sup. 13 (4) (1981), 465-480. | Numdam | MR 654208 | Zbl 0491.58015

[5] J. J. Duistermaat, On global action-angle coordinates, Comm. Pure Appl. Math. XXXIII (1980) 687-706. | MR 596430 | Zbl 0439.58014

[6] D. Fried - W. Goldman - M. W. Hirsch, Affine manifolds with nilpotent holonomy, Comm. Math. Helv. 56 (1981), 487-523. | MR 656210 | Zbl 0516.57014

[7] A. Haefliger, Some remarks on foliations with minimal leaves, J. Differential Geom. 15 (1980), 269-284. | MR 614370 | Zbl 0444.57016

[8] N. H. Kuiper, Sur les surfaces localement affines, Colloque de Géom. Diff. Strasbourg (1953). | MR 60288 | Zbl 0053.13003

[9] T. Nagano - K. Yagi, The affine structures on the real two-torus (I), Osaka J. Math. 11 (1974), 181-210. | MR 377917 | Zbl 0285.53030

[10] A. Weinstein, “Lectures on symplectic manifolds”, Regional Conference Series in Mathematics, AMS (1976). | MR 464312 | Zbl 0406.53031