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

Liviu Ornea; Misha Verbitsky

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arXiv · 1702.00985

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

Liviu Ornea·Misha Verbitsky

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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.

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BibTeX RIS

Liviu Ornea, Misha Verbitsky. 2017-02-03. Embedding of LCK manifolds with potential into Hopf manifolds using Riesz-Schauder theorem. https://arxiv.org/abs/1702.00985

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