Classification of real analytic Levi flat hypersurfaces of 1-concave type in Hopf surfaces

Abstract

A compact Levi flat hypersurface in a complex manifold is said to be of $q$-concave type if it admits a neighborhood system consisting of $q$-concave manifolds in the sense of Andreotti and Grauert. The real analytic Levi flat hypersurfaces of $1$-concave type in Hopf surfaces are classified.