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

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• 作者：Deroin ; Bertrand
• 刊名：Comptes Rendus Mathematique
• 出版年：2003
• 期刊代码：64_1631073x
• 类别：mt
• 出版时间：December 15, 2003
• 卷：337
• 期：1
• 页码：777-780
• 文件大小：86.9 K

摘要

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).