On the dynamics of foliations in ${\mathbb{P}}^n$ tangent to Levi-flat hypersurfaces

Abstract

Let $\mathcal{F}$ be a codimension one holomorphic foliation in ${\mathbb{P}}^n$, $n\ge 2$, leaving invariant a real-analytic Levi-flat hypersurface $M$ with regular part $M^{\ast }$. Then every leaf of $\mathcal{F}$ outside $\overline{M^{\ast }}$ accumulates in $\overline{M^{\ast }}$.

9 pages