Embedding of LCK manifolds with potential into Hopf manifolds using Riesz-Schauder theorem
Differential Geometry
2020-07-30 v2 Algebraic Geometry
Complex Variables
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.
Keywords
Cite
@article{arxiv.1702.00985,
title = {Embedding of LCK manifolds with potential into Hopf manifolds using Riesz-Schauder theorem},
author = {Liviu Ornea and Misha Verbitsky},
journal= {arXiv preprint arXiv:1702.00985},
year = {2020}
}
Comments
14 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