no. 5
J-holomorphic discs and real analytic hypersurfaces
[Disques J-holomorphes et hypersurfaces réelles analytiques]
Alexandre, William1 ; Mazzilli, Emmanuel1
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.
Annales de l'Institut Fourier, Tome 64 (2014) no. 5, pp. 2223-2250.

Nous définissons dans ℝ 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.

We give in ℝ 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.

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. 
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Alexandre, William; Mazzilli, Emmanuel. $J$-holomorphic discs and real analytic hypersurfaces. Annales de l'Institut Fourier, Tome 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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