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

preprint2014arXivOpen access

Abstract

Let F\mathcal{F} be a codimension one holomorphic foliation in Pn\mathbb{P}^n, n≥2n\geq 2, leaving invariant a real-analytic Levi-flat hypersurface MM with regular part M∗M^{*}. Then every leaf of F\mathcal{F} outside M∗‾\overline{M^{*}} accumulates in M∗‾\overline{M^{*}}.

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