Hypersurfaces Levi-plates immergées dans les surfaces complexes de courbure positive

Bertrand Deroin

doi:10.1016/j.crma.2003.09.016

Hypersurfaces Levi-plates immergées dans les surfaces complexes de courbure positive

Translated title of the contribution: Levi-flat hypersurfaces immerged in complex surfaces of positive curvature

Bertrand Deroin

CNRS UMR 5669, 'Unité de Mathématiques Pures et Appliquées' and project-team Inria NUMED, Ecole Normale Supérieure de Lyon

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that there is no Levi-flat immersion of class C¹ of a Riemann surface foliation of class C¹ of a 3-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 C¹ 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).

Translated title of the contribution	Levi-flat hypersurfaces immerged in complex surfaces of positive curvature
Original language	French
Pages (from-to)	777-780
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	337
Issue number	12
DOIs	https://doi.org/10.1016/j.crma.2003.09.016
Publication status	Published - 15 Dec 2003
Externally published	Yes

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abstract = "We prove that there is no Levi-flat immersion of class C1 of a Riemann surface foliation of class C1 of a 3-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 C1 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).",

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AB - We prove that there is no Levi-flat immersion of class C1 of a Riemann surface foliation of class C1 of a 3-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 C1 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).

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Hypersurfaces Levi-plates immergées dans les surfaces complexes de courbure positive

Abstract

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