Local Levi-flat hypersurfaces invariants by a codimension one holomorphic foliation

Abstract

In this paper we study codimension one holomorphic foliations leaving invariant real analytic hypersurfaces. In particular, we prove that a germ of real analytic Levi-flat hypersurface with sufficiently ``small" singular set is given by the zeroes of the imaginary part of a holomorphic function.