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- W4309208844 abstract "An LCK (locally conformally Kahler) manifold is a Hermitian manifold which admits a Kahler cover with deck group acting by holomorphic homotheties with respect to the Kahler metric. The product of two LCK manifolds does not have a natural product LCK structure. It is conjectured that a product of two compact complex manifolds is never LCK. We classify all known examples of compact LCK manifolds onto three exclusive classes: LCK with potential, Oeljeklaus-Toma, and those containing a rational curve. In the present paper, we prove that a product of an LCK manifold and an LCK manifold belonging to one of these three classes does not admit an LCK structure." @default.
- W4309208844 created "2022-11-24" @default.
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- W4309208844 date "2022-11-15" @default.
- W4309208844 modified "2023-09-27" @default.
- W4309208844 title "Do products of compact complex manifolds admit LCK metrics?" @default.
- W4309208844 doi "https://doi.org/10.48550/arxiv.2211.08111" @default.
- W4309208844 hasPublicationYear "2022" @default.
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