A note on projective Levi flats and minimal sets of algebraic foliations

Neto, Alcides Lins

Annales de l'Institut Fourier, Tome 49 (1999) no. 4, pp. 1369-1385.

Dans cet article on démontre qu’un feuilletage holomorphe de codimension un dans $ℂ{\mathbb{P}}^n,n\ge 3$, n’a pas de minimaux non triviaux. On démontre aussi que pour $n\ge 3$, il n’existe pas de surfaces de Levi plates, analytiques réelles, dans $ℂ{\mathbb{P}}^n$.

In this paper we prove that holomorphic codimension one singular foliations on $ℂ{\mathbb{P}}^n,n\ge 3$ have no non trivial minimal sets. We prove also that for $n\ge 3$, there is no real analytic Levi flat hypersurface in $ℂ{\mathbb{P}}^n$.

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