Nonexistence of Levi flat hypersurfaces with positive normal bundle in compact Kähler manifolds of dimension ≥3-Reference-Cited by-同舟云学术

Nonexistence of Levi flat hypersurfaces with positive normal bundle in compact Kähler manifolds of dimension ≥3

Published:2019-12-04 Issue:01 Volume:31 Page:2050004
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

Biard Séverine¹,Iordan Andrei²

Affiliation:

1. Institut de Mathématiques, UMR 7586 du CNRS, Case 247, Université Pierre et Marie-Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France

2. Sorbonne Université, Faculté des Sciences et Ingénierie, Institut de Mathématiques de Jussieu-Paris Rive Gauche, 4 Place Jussieu, 75252 Paris Cedex 05, France

Abstract

Let [Formula: see text] be a compact connected Kähler manifold of dimension [Formula: see text] and [Formula: see text] a [Formula: see text] Levi flat hypersurface in [Formula: see text]. Then the normal bundle to the Levi foliation does not admit a Hermitian metric with positive curvature along the leaves. This represents an answer to a conjecture of Marco Brunella.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X20500044

Reference31 articles.

1. Carleman estimates for the laplace-beltrami equation on complex manifolds

2. On the smoothness of Levi-foliations

3. Sur les courbes définies par des équations différentielles

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