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

## TL;DR

This paper proves that LCK manifolds with potential can be embedded into Hopf manifolds using functional analysis, specifically the Riesz-Schauder theorem, and provides an alternative proof for complex surfaces.

## Contribution

It introduces a functional-analytic proof for embedding LCK manifolds with potential into Hopf manifolds, extending previous results.

## Key findings

- Embedding of LCK manifolds with potential into Hopf manifolds for dimension ≥ 3
- Functional-analytic proof based on Riesz-Schauder theorem
- Alternative proof for complex surfaces using the Spherical Shell Conjecture

## 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.