Une caractérisation des formes symplectiques

Bruno Sévennec

Annales de l'institut Fourier (1998)

  • Volume: 48, Issue: 1, page 265-280
  • ISSN: 0373-0956

Abstract

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It is shown that a nonzero 2-form on a manifold M , such that the pseudogroup of local diffeomorphisms preserving it acts transitively on the bundle of tangent directions, is symplectic if dim M is not 6 . Moreover, there is a counterexample in 6 dimensions, which is shown to be essentially unique.

How to cite

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Sévennec, Bruno. "Une caractérisation des formes symplectiques." Annales de l'institut Fourier 48.1 (1998): 265-280. <http://eudml.org/doc/75279>.

@article{Sévennec1998,
abstract = {On montre qu’une 2-forme non nulle sur une variété $M$, telle que le pseudogroupe des difféomorphismes locaux la préservant soit transitif sur le fibré des directions tangentes, est symplectique si la dimension de $M$ n’est pas $6$. De plus, il y a un contre-exemple en dimension 6, dont on montre qu’il est essentiellement unique.},
author = {Sévennec, Bruno},
journal = {Annales de l'institut Fourier},
keywords = {symplectic form; pseudogroup; transitive action},
language = {fre},
number = {1},
pages = {265-280},
publisher = {Association des Annales de l'Institut Fourier},
title = {Une caractérisation des formes symplectiques},
url = {http://eudml.org/doc/75279},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Sévennec, Bruno
TI - Une caractérisation des formes symplectiques
JO - Annales de l'institut Fourier
PY - 1998
PB - Association des Annales de l'Institut Fourier
VL - 48
IS - 1
SP - 265
EP - 280
AB - On montre qu’une 2-forme non nulle sur une variété $M$, telle que le pseudogroupe des difféomorphismes locaux la préservant soit transitif sur le fibré des directions tangentes, est symplectique si la dimension de $M$ n’est pas $6$. De plus, il y a un contre-exemple en dimension 6, dont on montre qu’il est essentiellement unique.
LA - fre
KW - symplectic form; pseudogroup; transitive action
UR - http://eudml.org/doc/75279
ER -

References

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