Geodesic
Levi-flat world: a survey of local theory
Ufa mathematical journal, Tome 9 (2017) no. 3, pp. 172-185

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This expository paper concerns local properties of Levi-flat real analytic manifolds with singularities. Levi-flat manifolds arise naturally in Complex Geometry and Foliation Theory. In many cases (global) compact Levi-flat manifolds without singularities do not exist. These global obstructions make natural the study of Levi-flat objects with singularities because they always exist. The present expository paper deals with some recent results on local geometry of Levi-flat singularities. One of the main questions concerns an extension of the Levi foliation as a holomorphic foliation to a full neighborhood of singularity. It turns out that in general such extension does not exist. Nevertheless, the Levi foliation always extends as a holomorphic web (a foliation with branching) near a non-dicritical singularity. We also present an efficient criterion characterizing these singularities.
Keywords: Levi-flat manifold.
Mots-clés : CR structure 
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     author = {A. Sukhov},
     title = {Levi-flat world: a survey of local theory},
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A. Sukhov. Levi-flat world: a survey of local theory. Ufa mathematical journal, Tome 9 (2017) no. 3, pp. 172-185. http://geodesic.mathdoc.fr/item/UFA_2017_9_3_a17/