no. 1
Liouville forms in a neighborhood of an isotropic embedding
Annales de l'Institut Fourier, Tome 47 (1997) no. 1, pp. 257-272

A Liouville form on a symplectic manifold (X,ω) is by definition a potential β of the symplectic form -dβ=ω. Its center M is given by β -1 (0). A normal form for certain Liouville forms in a neighborhood of its center is given.

Une forme de Liouville sur une variété symplectique (X,ω) est un potentiel β de la forme symplectique -dβ=ω. Son centre M est β -1 (0). Nous présentons une forme normale de β dans un voisinage de M.

@article{AIF_1997__47_1_257_0,
     author = {Loose, Frank},
     title = {Liouville forms in a neighborhood of an isotropic embedding},
     journal = {Annales de l'Institut Fourier},
     pages = {257--272},
     year = {1997},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {47},
     number = {1},
     doi = {10.5802/aif.1566},
     zbl = {0860.53019},
     mrnumber = {98c:53040},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1566/}
}
TY  - JOUR
AU  - Loose, Frank
TI  - Liouville forms in a neighborhood of an isotropic embedding
JO  - Annales de l'Institut Fourier
PY  - 1997
SP  - 257
EP  - 272
VL  - 47
IS  - 1
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1566/
DO  - 10.5802/aif.1566
LA  - en
ID  - AIF_1997__47_1_257_0
ER  - 
%0 Journal Article
%A Loose, Frank
%T Liouville forms in a neighborhood of an isotropic embedding
%J Annales de l'Institut Fourier
%D 1997
%P 257-272
%V 47
%N 1
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1566/
%R 10.5802/aif.1566
%G en
%F AIF_1997__47_1_257_0
Loose, Frank. Liouville forms in a neighborhood of an isotropic embedding. Annales de l'Institut Fourier, Tome 47 (1997) no. 1, pp. 257-272. doi: 10.5802/aif.1566

[EG] Y. Eliashberg, M. Gromov, Convex symplectic manifolds, Proceedings of Symposia in Pure Mathematics, 52, part 2 (1991), 135-162. | Zbl | MR

[GuSt] V. Guillemin and S. Sternberg, Geometric asymptotics, AMS Providence, Rhode Island, 1977. | Zbl | MR

[Ha] P. Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York, 1964. | Zbl | MR

[Lo] F. Loose, Neighborhood geometry of isotropic embeddings, Habilitationsschrift, Verlag Dr. Köster, Berlin, 1996. | Zbl

[SjLe] R. Sjamaar and E. Lerman, Stratified symplectic spaces and reduction, Ann. Math., 134 (1991), 375-422. | Zbl | MR

[We1] A. Weinstein, Lectures on symplectic manifolds, CBMS Regional Conf. Series in Math., 29, 1977. | Zbl | MR

[We2] A. Weinstein, Neighborhood classification of isotropic embeddings, J. Differ. Geom., 16 (1981), 125-128. | Zbl | MR

Cité par Sources :