$J$-holomorphic discs and real analytic hypersurfaces

Alexandre, William; Mazzilli, Emmanuel

J

-holomorphic discs and real analytic hypersurfaces
[Disques

J

-holomorphes et hypersurfaces rÃ©elles analytiques]

Alexandre, William ; Mazzilli, Emmanuel

Annales de l'Institut Fourier, Tome 64 (2014), p. 2223-2250 / Harvested from Numdam

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Résumé
Abstract

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 $\frac{\partial γ}{\partial x} (0) = v$ . 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 $\frac{\partial γ}{\partial x} (0) = v$ , 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.

Publié le : 2014-01-01

MR 3330937 | Zbl 06387337

DOI : https://doi.org/10.5802/aif.2910
Classification: 32Q60, 32Q65
Mots clés: Structure presque complexe, disque

J

-holomorphe, 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},
     volume = {64},
     year = {2014},
     pages = {2223-2250},
     doi = {10.5802/aif.2910},
     zbl = {06387337},
     mrnumber = {3330937},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2014__64_5_2223_0}
}

Alexandre, William; Mazzilli, Emmanuel. $J$-holomorphic discs and real analytic hypersurfaces. Annales de l'Institut Fourier, Tome 64 (2014) pp. 2223-2250. doi : 10.5802/aif.2910. http://gdmltest.u-ga.fr/item/AIF_2014__64_5_2223_0/

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