Non-linear Hopf manifolds are locally conformally Kahler
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866914804134838272 |
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| author | Ornea, Liviu Verbitsky, Misha |
| author_facet | Ornea, Liviu Verbitsky, Misha |
| contents | A Hopf manifold is a quotient of $C^n\backslash 0$ by the cyclic group generated by a holomorphic contraction. Hopf manifolds are diffeomorphic to $S^1\times S^{2n-1}$ and 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 defined by non-linear holomorphic contractions admit holomorphic embeddings into linear Hopf manifolds, and, moreover they admit LCK metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_12398 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-linear Hopf manifolds are locally conformally Kahler Ornea, Liviu Verbitsky, Misha Differential Geometry Complex Variables A Hopf manifold is a quotient of $C^n\backslash 0$ by the cyclic group generated by a holomorphic contraction. Hopf manifolds are diffeomorphic to $S^1\times S^{2n-1}$ and 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 defined by non-linear holomorphic contractions admit holomorphic embeddings into linear Hopf manifolds, and, moreover they admit LCK metrics. |
| title | Non-linear Hopf manifolds are locally conformally Kahler |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2202.12398 |