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Comptes Rendus Mathématique
Volume 337, n° 12
pages 777-780 (décembre 2003)
Doi : 10.1016/j.crma.2003.09.016
Received : 8 September 2003 ; 
Hypersurfaces Levi-plates immergées dans les surfaces complexes de courbure positive
Levi-flat hypersurfaces immerged in complex surfaces of positive curvature

Bertrand  Deroin
Unité de mathématiques pures et appliquées, École normale supérieure de Lyon, UMR 5669 CNRS, 46, allée d'Italie, 69364 Lyon cedex 07, France 

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Nous démontrons qu'il n'y a pas d'immersion Levi-plate de classe   d'un feuilletage par surfaces de Riemann de classe   d'une variété compacte de dimension   dans le plan projectif complexe, si le feuilletage possède un courant harmonique absolument continu par rapport à la mesure de Lebesgue, avec une densité bornée supérieurement et inférieurement. Ceci découle d'un résultat de rigidité pour les immersions Levi-plates d'un feuilletage ayant la même régularité, à valeurs dans une surface complexe de courbure de Ricci positive ou nulle. Pour citer cet article : B. Deroin, C. R. Acad. Sci. Paris, Ser. I 337 (2003).

Abstract

We prove that there is no Levi-flat immersion of class   of a Riemann surface foliation of class   of a  -dimensional compact manifold in the complex projective plane, if the foliation carries a harmonic current which is absolutely continuous with respect to Lebesgue measure, with a density bounded from above and below. This comes as a corollary of a rigidity result for Levi-flat immersions of class   of Riemann surface foliations having this regularity into complex surfaces of non negative Ricci curvature. To cite this article: B. Deroin, C. R. Acad. Sci. Paris, Ser. I 337 (2003).




© 2003  Académie des sciences@@#104156@@

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