Calabi-Yau locally conformally Kähler manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914184270184448 |
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| author | Barbaro, Giuseppe Otiman, Alexandra |
| author_facet | Barbaro, Giuseppe Otiman, Alexandra |
| contents | We study compact locally conformally Kähler (lcK) manifolds which are Calabi--Yau, in the sense that $c_1^{BC}(X)=0$. First of all, we prove that all the known lcK manifolds which are Calabi--Yau are Vaisman. Then we prove that an lcK Chern--Ricci flat metric that is Gauduchon is necessarily Vaisman. Finally, specializing to Calabi--Yau solvmanifolds with left-invariant complex structure, we prove that a left-invariant metric is lcK if and only if it is Vaisman. Therefore, they are finite quotients of the Kodaira manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Calabi-Yau locally conformally Kähler manifolds Barbaro, Giuseppe Otiman, Alexandra Differential Geometry We study compact locally conformally Kähler (lcK) manifolds which are Calabi--Yau, in the sense that $c_1^{BC}(X)=0$. First of all, we prove that all the known lcK manifolds which are Calabi--Yau are Vaisman. Then we prove that an lcK Chern--Ricci flat metric that is Gauduchon is necessarily Vaisman. Finally, specializing to Calabi--Yau solvmanifolds with left-invariant complex structure, we prove that a left-invariant metric is lcK if and only if it is Vaisman. Therefore, they are finite quotients of the Kodaira manifold. |
| title | Calabi-Yau locally conformally Kähler manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2509.18364 |