Embedding of LCK manifolds with potential into Hopf manifolds using Riesz-Schauder theorem

Abstract

An locally conformally Kahler (LCK) manifold with potential is a complex manifold with a cover which admits an automorphic Kahler potential. An LCK manifold with potential can be embedded to a Hopf manifold, if its dimension is at least 3. We give a functional-analytic proof of this result based on Riesz-Schauder theorem and Montel theorem. We give an alternative argument for complex surfaces, deducing embedding theorem from the Spherical Shell Conjecture.

arXiv comment14 pages. Minor corrections and bibliography added. Version accepted as contribution to the proceedings of the "INdAM Meeting Complex and Symplectic Geometry" held in Cortona 2016