An Aubin-Yau theorem for transversally Kähler foliations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908393324675072 |
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| author | Marchidanu, Vlad |
| author_facet | Marchidanu, Vlad |
| contents | Transversally Kähler foliations are a generalisation of Kähler manifolds, appearing naturally in the complex non-Kähler setting. We give a self-contained proof of how the classical methods used in the proof of the Aubin-Yau theorem adapt to the transversally Kähler case under the homological orientability condition. We apply this result to obtain a new, simpler proof of the already known Vaisman Aubin-Yau theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03987 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Aubin-Yau theorem for transversally Kähler foliations Marchidanu, Vlad Differential Geometry Analysis of PDEs Complex Variables 53C55, 32J27, 58J05, 32M25 Transversally Kähler foliations are a generalisation of Kähler manifolds, appearing naturally in the complex non-Kähler setting. We give a self-contained proof of how the classical methods used in the proof of the Aubin-Yau theorem adapt to the transversally Kähler case under the homological orientability condition. We apply this result to obtain a new, simpler proof of the already known Vaisman Aubin-Yau theorem. |
| title | An Aubin-Yau theorem for transversally Kähler foliations |
| topic | Differential Geometry Analysis of PDEs Complex Variables 53C55, 32J27, 58J05, 32M25 |
| url | https://arxiv.org/abs/2506.03987 |