LEVI-FLAT HYPERSURFACE INTO POSITIVELY CURVED COMPLEX SURFACES

Abstract. We prove that there is no Levi-flat immersion of class C1 of a Rie-mann surface foliation of class C1 of a 3-dimensional compact manifold into the complex projective space, if the foliation carries a harmonic current abso-lutely continuous with respect to Lebesgue measure, with a density bounded from above and below. We give also rigidity results for Levi-flat immersion of class C1 of such Riemann surface foliation into complex surface of positive curvature