On the normal bundle of Levi-flat real hypersurfaces

Abstract

Let $X$ be a connected complex manifold of dimension $\ge 3$ 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.

minor changes, final version, in Math. Ann. (online first)

References in corpus (2)

• Curvature restrictions for Levi-flat real hypersurfaces in complex projective planes
• A local expression of the Diederich--Fornaess exponent and the exponent of conformal harmonic measures

Cited by in corpus (1)

• Diederich-Fornaess and Steinness indices for abstract CR manifolds