On the normal bundle of Levi-flat real hypersurfaces

2018/04/30 by Judith Brinkschulte · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Complex manifold #Foliation (geology) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Hermitian manifold #Hermitian matrix #Hypersurface #Manifold (fluid mechanics) #Metric (unit) #Normal bundle #math.CV #math.DG #math.DS #msc:32V15 #msc:32V40

paper · pdf · doi:10.1007/s00208-018-1723-7

published as Math. Ann. 375, 343--359 (2019) · minor changes, final version, in Math. Ann. (online first)

openalex created_date 2018/04/24 · openalex publication_date 2018/07/06 · arxiv created 2018/07/23 · arxiv updated 2019/09/25 · openalex updated_date 2026/08/05

Abstract

Let X be a connected complex manifold of dimension ≥ 3 and M a smooth compact Levi-flat real hypersurface in X. We show that the normal bundle to the Levi foliation does not admit a Hermitian metric with positive curvature along the leaves. This generalizes a result obtained by Brunella.

Citations

• Bemerkenswerte pseudokonvexe Mannigfaltigkeiten
• A Stein Domain with Smooth Boundary Which Has a Product Structure
• L² Approaches in Several Complex Variables

Cited by

• On holomorphic foliations admitting invariant CR manifolds