2014/10/31 by Masanori Adachi, Judith Brinkschulte · 16 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Curvature #Foliation (geology) #Geology #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Holomorphic function #Hypersurface #Infinitesimal #Mathematical analysis #Mathematics #Mean curvature #Pure mathematics #Ricci curvature #math.CV #math.DG #math.DS #msc:32V15 #msc:32V40 #msc:53B25 #msc:53C12
paper · pdf · doi:10.5802/aif.2995
published in Annales de l’institut Fourier 65(6), 2547-2569 (Association of the Annals of the Fourier Institute) · 19 pages, final version, to appear in Annales de l'Institut Fourier
arxiv created 2015/02/27 · openalex publication_date 2015/12/07 · arxiv updated 2016/01/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study curvature restrictions of Levi-flat real hypersurfaces in complex projective planes, whose existence is in question. We focus on its totally real Ricci curvature, the Ricci curvature of the real hypersurface in the direction of the Reeb vector field, and show that it cannot be greater than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> along a Levi-flat real hypersurface. We rely on a finiteness theorem for the space of square integrable holomorphic 2-forms on the complement of the Levi-flat real hypersurface, where the curvature plays the role of the size of the infinitesimal holonomy of its Levi foliation.