Non existence of Levi flat hypersurfaces with positive normal bundle in compact Kähler manifolds of dimension at least 3

Abstract

We prove that the normal bundle to the Levi foliation of a smooth Levi flat hypersurface does not admit a Hermitian metric with positive curvature along the leaves in compact Kähler manifolds of dimension at least 3. This represents an answer to a conjecture of Marco Brunella.

to be published in International Journal of Mathematics, 2020

Cited by in corpus (1)

• A CR proof for a global estimate of the Diederich--Fornaess index of Levi-flat real hypersurfaces