Appears in collection : Conférence à la mémoire de Jean-Pierre Demailly

Numerical Bogomolov sheaves are rank one coherent subsheaves L of ΩpX having numerical dimension p for some p > 0, and a complex projective (or more generally compact Kähler) manifold X. The existence of L like above determines a distribution D, namely the kernel of L. According to a theorem of Jean-Pierre Demailly, this distribution is actually integrable. The main part of this talk will be devoted to questions (essentially unsolved) concerning the structure of this foliation and are motivated on one hand by some results concerning the case p=1, on the other hand by a recent joint work with Benoît Claudon.