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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2405.05604 |
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| _version_ | 1866913684191707136 |
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| author | Nakagawa, Yasuhiro Nakamura, Satoshi |
| author_facet | Nakagawa, Yasuhiro Nakamura, Satoshi |
| contents | Motivated by the notion of multiplier Hermitian-Einstein metric of type $σ$ introduced by Mabuchi, we introduce the notion of $σ$-extremal Kähler metrics on compact Kähler manifolds, which generalizes Calabi's extremal Kähler metrics. We characterize the existence of this metric in terms of the coercivity of a certain functional on the space of Kähler metrics to show that, on a Fano manifold, the existence of a multiplier Hermitian-Einstein metric of type $σ$ implies the existence of a $σ$-extremal Kähler metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05604 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modified extremal Kähler metrics and multiplier Hermitian-Einstein metrics Nakagawa, Yasuhiro Nakamura, Satoshi Differential Geometry Motivated by the notion of multiplier Hermitian-Einstein metric of type $σ$ introduced by Mabuchi, we introduce the notion of $σ$-extremal Kähler metrics on compact Kähler manifolds, which generalizes Calabi's extremal Kähler metrics. We characterize the existence of this metric in terms of the coercivity of a certain functional on the space of Kähler metrics to show that, on a Fano manifold, the existence of a multiplier Hermitian-Einstein metric of type $σ$ implies the existence of a $σ$-extremal Kähler metric. |
| title | Modified extremal Kähler metrics and multiplier Hermitian-Einstein metrics |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2405.05604 |