Disques J-holomorphes contenus dans une hypersurface

Abstract

We study germs of J-Holomorphic curves contained in $M$, a real analytic hypersurface of an symplectic manifold of dimension 4. We show, under topological hypothesis on $M$, that if $M$ is compact then $M$ is of finite type and so there is no germs of $J$-holomorphic curves on $M$(with $J$ adapted with the symplectic form). In ${\mathbb{C}}^2$ with the standard complex structure, this is a classical result of Diederich-Fornaess.