Une caractérisation des formes symplectiques
Annales de l'Institut Fourier, Volume 48 (1998) no. 1, p. 265-280

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.

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.

@article{AIF_1998__48_1_265_0,
     author = {S\'evennec, Bruno},
     title = {Une caract\'erisation des formes symplectiques},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {48},
     number = {1},
     year = {1998},
     pages = {265-280},
     doi = {10.5802/aif.1618},
     zbl = {0943.53047},
     mrnumber = {99b:53047},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1998__48_1_265_0}
}
Sévennec, Bruno. Une caractérisation des formes symplectiques. Annales de l'Institut Fourier, Volume 48 (1998) no. 1, pp. 265-280. doi : 10.5802/aif.1618. http://www.numdam.org/item/AIF_1998__48_1_265_0/

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