All toric Hermitian ALE gravitational instantons
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917002974593024 |
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| author | Araneda, Bernardo Lucietti, James |
| author_facet | Araneda, Bernardo Lucietti, James |
| contents | We prove that the only smooth, Ricci flat, ALE instanton with a toric Hermitian non-Kähler structure is the Eguchi-Hanson instanton. The proof is analogous to the classification of toric Hermitian ALF instantons by Biquard and Gauduchon, although we avoid the use of toric Kähler geometry and instead perform a direct global analysis of the Tod form of the metric in Weyl-Papapetrou coordinates. This supports a conjecture by Gibbons and Bando-Kasue-Nakajima which states that any Ricci flat ALE instanton is self-dual. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09291 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | All toric Hermitian ALE gravitational instantons Araneda, Bernardo Lucietti, James Differential Geometry General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We prove that the only smooth, Ricci flat, ALE instanton with a toric Hermitian non-Kähler structure is the Eguchi-Hanson instanton. The proof is analogous to the classification of toric Hermitian ALF instantons by Biquard and Gauduchon, although we avoid the use of toric Kähler geometry and instead perform a direct global analysis of the Tod form of the metric in Weyl-Papapetrou coordinates. This supports a conjecture by Gibbons and Bando-Kasue-Nakajima which states that any Ricci flat ALE instanton is self-dual. |
| title | All toric Hermitian ALE gravitational instantons |
| topic | Differential Geometry General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2510.09291 |