J-holomorphic discs and real analytic hypersurfaces
Annales de l'Institut Fourier, Volume 64 (2014) no. 5, pp. 2223-2250.

We give in 6 a real analytic almost complex structure J, a real analytic hypersurface M and a vector v in the Levi null set at 0 of M, such that there is no germ of J-holomorphic disc γ included in M with γ(0)=0 and γ x(0)=v, although the Levi form of M has constant rank. Then for any hypersurface M and any complex structure J, we give sufficient conditions under which there exists such a germ of disc.

Nous définissons dans 6 une structure presque complexe réelle analytique J, une hypersurface réelle analytique M dont la forme de Levi est de rang constant et un vecteur v appartenant au noyau de la forme de Levi de M en 0 tels qu’il n’existe pas de germe de disque J-holomorphe γ inclus dans M vérifiant γ(0)=0 et γ x(0)=v. Nous donnons ensuite des conditions suffisantes pour qu’un tel germe de disque existe.

DOI: 10.5802/aif.2910
Classification: 32Q60, 32Q65
Keywords: almost complex structure, $J$-holomorphic disc, hypersurface
Mot clés : Structure presque complexe, disque $J$-holomorphe, hypersurface
Alexandre, William 1; Mazzilli, Emmanuel 1

1 Laboratoire Paul Painlevé U.M.R. CNRS 8524 U.F.R. de Mathématiques cité scientifique Université Lille 1 F59 655 Villeneuve d’Ascq Cedex, France.
     author = {Alexandre, William and Mazzilli, Emmanuel},
     title = {$J$-holomorphic discs and real analytic hypersurfaces},
     journal = {Annales de l'Institut Fourier},
     pages = {2223--2250},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {64},
     number = {5},
     year = {2014},
     doi = {10.5802/aif.2910},
     mrnumber = {3330937},
     zbl = {06387337},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2910/}
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JO  - Annales de l'Institut Fourier
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PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.2910/
DO  - 10.5802/aif.2910
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Alexandre, William; Mazzilli, Emmanuel. $J$-holomorphic discs and real analytic hypersurfaces. Annales de l'Institut Fourier, Volume 64 (2014) no. 5, pp. 2223-2250. doi : 10.5802/aif.2910. https://aif.centre-mersenne.org/articles/10.5802/aif.2910/

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