It is shown that a nonzero 2-form on a manifold , such that the pseudogroup of local diffeomorphisms preserving it acts transitively on the bundle of tangent directions, is symplectic if is not . Moreover, there is a counterexample in dimensions, which is shown to be essentially unique.
On montre qu’une 2-forme non nulle sur une variété , telle que le pseudogroupe des difféomorphismes locaux la préservant soit transitif sur le fibré des directions tangentes, est symplectique si la dimension de n’est pas . 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}, pages = {265--280}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {48}, number = {1}, year = {1998}, doi = {10.5802/aif.1618}, zbl = {0943.53047}, mrnumber = {99b:53047}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1618/} }
TY - JOUR AU - Sévennec, Bruno TI - Une caractérisation des formes symplectiques JO - Annales de l'Institut Fourier PY - 1998 SP - 265 EP - 280 VL - 48 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1618/ DO - 10.5802/aif.1618 LA - fr ID - AIF_1998__48_1_265_0 ER -
%0 Journal Article %A Sévennec, Bruno %T Une caractérisation des formes symplectiques %J Annales de l'Institut Fourier %D 1998 %P 265-280 %V 48 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1618/ %R 10.5802/aif.1618 %G fr %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.1618/
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