Generalized almost-Kähler-Ricci solitons
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910319759065088 |
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| author | Albanese, Michael Barbaro, Giuseppe Lejmi, Mehdi |
| author_facet | Albanese, Michael Barbaro, Giuseppe Lejmi, Mehdi |
| contents | We generalize Kähler-Ricci solitons to the almost-Kähler setting as the zeros of Inoue's moment map \cite{MR4017922}, and show that their existence is an obstruction to the existence of first-Chern-Einstein almost-Kähler metrics on compact symplectic Fano manifolds. We prove deformation results of such metrics in the $4$-dimensional case. Moreover, we study the Lie algebra of holomorphic vector fields on $2n$-dimensional compact symplectic Fano manifolds admitting generalized almost-Kähler-Ricci solitons. In particular, we partially extend Matsushima's theorem \cite{MR0094478} to compact first-Chern-Einstein almost-Kähler manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03996 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized almost-Kähler-Ricci solitons Albanese, Michael Barbaro, Giuseppe Lejmi, Mehdi Differential Geometry Complex Variables 53C55 (primary), 53B35 (secondary) We generalize Kähler-Ricci solitons to the almost-Kähler setting as the zeros of Inoue's moment map \cite{MR4017922}, and show that their existence is an obstruction to the existence of first-Chern-Einstein almost-Kähler metrics on compact symplectic Fano manifolds. We prove deformation results of such metrics in the $4$-dimensional case. Moreover, we study the Lie algebra of holomorphic vector fields on $2n$-dimensional compact symplectic Fano manifolds admitting generalized almost-Kähler-Ricci solitons. In particular, we partially extend Matsushima's theorem \cite{MR0094478} to compact first-Chern-Einstein almost-Kähler manifolds. |
| title | Generalized almost-Kähler-Ricci solitons |
| topic | Differential Geometry Complex Variables 53C55 (primary), 53B35 (secondary) |
| url | https://arxiv.org/abs/2402.03996 |