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Non-linear Hopf Manifolds are Locally Conformally Kähler
Journal of Geometric Analysis. 2023. Vol. 33. Article 201.
Ornea L., Verbitsky M.
A Hopf manifold is a quotient of Cn \0 by the cyclic group generated by a holomorphic contraction. Hopf manifolds are diffeomorphic to S1 × S2n−1 and hence do not admit Kähler metrics. It is known that Hopf manifolds defined by linear contractions (called linear Hopf manifolds) have locally conformally Kähler (LCK) metrics. In this paper, we prove that the Hopf manifolds defined by non-linear holomorphic contractions admit holomorphic embeddings into linear Hopf manifolds, and moreover, they admit LCK metrics.
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Singapore: Springer, 2025.
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Verbitsky M., Ornea L., / Series arXiv "math". 2022.
A Hopf manifold is a quotient of Cn∖0 by the cyclic group generated by a holomorphic contraction. Hopf manifolds are diffeomorphic to S1×S2n−1and hence do not admit Kahler metrics. It is known that Hopf manifolds defined by linear contractions (called linear Hopf manifolds) have locally conformally Kahler (LCK) metrics. In this paper we prove that the Hopf manifolds ...
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