On holomorphic foliations admitting invariant CR manifolds

We study holomorphic foliations of codimension $k\geq 1$ on a complex manifold $X$ dimension $n+k$ from the point view exceptional minimal set conjecture. For $n\geq 2$ we show in particular that if normal bundle $N_{\mathcal{F}}$ is Griffiths positive, then foliation does not admit compact invariant complete intersection $k$ smooth real hypersurfaces $X$.