J-holomorphic discs and real analytic hypersurfaces
Annales de l'Institut Fourier, Volume 64 (2014) no. 5, p. 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 : https://doi.org/10.5802/aif.2910
Classification:  32Q60,  32Q65
Keywords: almost complex structure, J-holomorphic disc, hypersurface
@article{AIF_2014__64_5_2223_0,
     author = {Alexandre, William and Mazzilli, Emmanuel},
     title = {$J$-holomorphic discs and real analytic hypersurfaces},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {5},
     year = {2014},
     pages = {2223-2250},
     doi = {10.5802/aif.2910},
     mrnumber = {3330937},
     zbl = {06387337},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2014__64_5_2223_0}
}
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. http://www.numdam.org/item/AIF_2014__64_5_2223_0/

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