Lagrangian holonomy ; characteristic elements of a lagrangian foliation

Carlos Currás-Bosch; Pierre Molino

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 2, page 319-326
  • ISSN: 0391-173X

Abstract

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Let ℒ be a lagrangian foliation on a symplectic manifold ( M 2 n , 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.

How to cite

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Currás-Bosch, Carlos, and Molino, Pierre. "Lagrangian holonomy ; characteristic elements of a lagrangian foliation." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.2 (2002): 319-326. <http://eudml.org/doc/84472>.

@article{Currás2002,
abstract = {Let $\mathcal \{L\}$ be a lagrangian foliation on a symplectic manifold $(M^\{2n\},\omega )$. 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.},
author = {Currás-Bosch, Carlos, Molino, Pierre},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {symplectic manifold; characteristic elements; compact leaf},
language = {eng},
number = {2},
pages = {319-326},
publisher = {Scuola normale superiore},
title = {Lagrangian holonomy ; characteristic elements of a lagrangian foliation},
url = {http://eudml.org/doc/84472},
volume = {1},
year = {2002},
}

TY - JOUR
AU - Currás-Bosch, Carlos
AU - Molino, Pierre
TI - Lagrangian holonomy ; characteristic elements of a lagrangian foliation
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2002
PB - Scuola normale superiore
VL - 1
IS - 2
SP - 319
EP - 326
AB - Let $\mathcal {L}$ be a lagrangian foliation on a symplectic manifold $(M^{2n},\omega )$. 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.
LA - eng
KW - symplectic manifold; characteristic elements; compact leaf
UR - http://eudml.org/doc/84472
ER -

References

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  1. [1] R. Bott, “Lectures on characteristic classes and foliations”, Lecture Notes in Math. 279 (1972). Zbl0241.57010MR362335
  2. [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. Zbl0939.53019MR1691432
  3. [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. Zbl0908.53010MR1649144
  4. [4] P. Dazord, Sur la géométrie des sous-fibrés et des feuilletages Lagrangiens, Ann. Sci. École Norm. Sup. 13 (4) (1981), 465-480. Zbl0491.58015MR654208
  5. [5] J. J. Duistermaat, On global action-angle coordinates, Comm. Pure Appl. Math. XXXIII (1980) 687-706. Zbl0439.58014MR596430
  6. [6] D. Fried – W. Goldman – M. W. Hirsch, Affine manifolds with nilpotent holonomy, Comm. Math. Helv. 56 (1981), 487-523. Zbl0516.57014MR656210
  7. [7] A. Haefliger, Some remarks on foliations with minimal leaves, J. Differential Geom. 15 (1980), 269-284. Zbl0444.57016MR614370
  8. [8] N. H. Kuiper, Sur les surfaces localement affines, Colloque de Géom. Diff. Strasbourg (1953). Zbl0053.13003MR60288
  9. [9] T. Nagano – K. Yagi, The affine structures on the real two-torus ( I ) , Osaka J. Math. 11 (1974), 181-210. Zbl0285.53030MR377917
  10. [10] A. Weinstein, “Lectures on symplectic manifolds”, Regional Conference Series in Mathematics, AMS (1976). Zbl0406.53031MR464312

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