Hermitian, Ricci-flat toric metrics on non-compact surfaces à la Biquard-Gauduchon
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913442885009408 |
|---|---|
| author | Oliveira, Gonçalo Sena-Dias, Rosa |
| author_facet | Oliveira, Gonçalo Sena-Dias, Rosa |
| contents | Biquard-Gauduchon have shown that conformally Kähler, Ricci-flat, ALF toric metrics on the complement of toric divisors are: the Taub-NUT metric with reversed orientation, in the Kerr-Taub-bolt family or in the Chen-Teo family. The same authors have also given a unified construction for the above families relying on an axi-symmetric harmonic function on $\mathbb{R}^3$. In this work, we reverse this construction and use methods from a paper of the second named author, "Uniqueness among scalar-flat Kähler metrics on non-compact toric 4-manifolds", to show that all conformally Kähler, Ricci-flat, toric metrics on the complement of toric divisors, under some mild assumptions on the associated moment polytope, are among the families above. In particular all such metrics are ALF. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16843 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hermitian, Ricci-flat toric metrics on non-compact surfaces à la Biquard-Gauduchon Oliveira, Gonçalo Sena-Dias, Rosa Differential Geometry 53C55, 53D20, 53C25 Biquard-Gauduchon have shown that conformally Kähler, Ricci-flat, ALF toric metrics on the complement of toric divisors are: the Taub-NUT metric with reversed orientation, in the Kerr-Taub-bolt family or in the Chen-Teo family. The same authors have also given a unified construction for the above families relying on an axi-symmetric harmonic function on $\mathbb{R}^3$. In this work, we reverse this construction and use methods from a paper of the second named author, "Uniqueness among scalar-flat Kähler metrics on non-compact toric 4-manifolds", to show that all conformally Kähler, Ricci-flat, toric metrics on the complement of toric divisors, under some mild assumptions on the associated moment polytope, are among the families above. In particular all such metrics are ALF. |
| title | Hermitian, Ricci-flat toric metrics on non-compact surfaces à la Biquard-Gauduchon |
| topic | Differential Geometry 53C55, 53D20, 53C25 |
| url | https://arxiv.org/abs/2407.16843 |