Kähler Soliton Surfaces Are Generically Toric
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908780104515584 |
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| author | Tran, Hung |
| author_facet | Tran, Hung |
| contents | Let $(M, g, ω, f, λ)$ be a Kähler gradient Ricci soliton in real dimension four. One first observes that it is an integrable Hamiltonian system in a classical sense. Indeed, all known complete examples are toric and the symmetry is intrinsically related to the potential function $f$ and the scalar curvature $\SS$. While another article addresses the case that these functions are functionally dependent, this one considers the independent case. The main result states that the soliton admits a toric action under a generic assumption. That is, one assumes that the system is non-degenerate and the potential function $f$ is proper. Then there is an effective, completely integrable Hamiltonian toric $\mathbb{T}^2$- action on $(M, ω)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kähler Soliton Surfaces Are Generically Toric Tran, Hung Differential Geometry 53E20, 53C25, 53D20 Let $(M, g, ω, f, λ)$ be a Kähler gradient Ricci soliton in real dimension four. One first observes that it is an integrable Hamiltonian system in a classical sense. Indeed, all known complete examples are toric and the symmetry is intrinsically related to the potential function $f$ and the scalar curvature $\SS$. While another article addresses the case that these functions are functionally dependent, this one considers the independent case. The main result states that the soliton admits a toric action under a generic assumption. That is, one assumes that the system is non-degenerate and the potential function $f$ is proper. Then there is an effective, completely integrable Hamiltonian toric $\mathbb{T}^2$- action on $(M, ω)$. |
| title | Kähler Soliton Surfaces Are Generically Toric |
| topic | Differential Geometry 53E20, 53C25, 53D20 |
| url | https://arxiv.org/abs/2404.18866 |