Nonexistence of Certain Levi Flat Hypersurfaces in Kähler Manifolds from the Viewpoint of Positive Normal Bundles

Abstract

Combining the $L^2$ method of solving the $\bar{\partial }$-equation with a method of Brunella in the study of Levi at hypersurfaces as stable sets of holomorphic foliations, two nonexistence theorems are proved for Levi flat hypersurfaces extending a result of Brunella.