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arXiv · 2311.01298

Almost holomorphic curves in real analytic hypersurfaces

Pierre Bonneau·Emmanuel Mazzilli
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Abstract

Using the theory of exterior differential systems, we study the existence of germ of pseudo-holomorphic disk in a real analytic hypersurface locally defined in a complex manifold equipped with J a real analytic almost complex structure. The integrable case in C n with J the multiplication by i has been intensively studied by several authors [DF], [DA1] and [DA2] for example. The non integrable case is drastically different essentially due to the following fact : in generic case, there is no J-invariant objects of dimension bigger than one. This simple observation leads to the non existence of some equivalents of Segree varieties or ideals of holomorphic functions which play a fundamental role in the complex case. Nevertheless in the almost complex case, we adopt the exterior differential system point of view of E.Cartan developed and clarified in [BCGGG].

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Pierre Bonneau, Emmanuel Mazzilli. 2023-11-02. Almost holomorphic curves in real analytic hypersurfaces. https://arxiv.org/abs/2311.01298

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