Twins in K{ä}hler and Sasaki geometry
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912127981191168 |
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| author | Boyer, Charles P. Huang, Hongnian Legendre, Eveline Tønnesen-Friedman, Christina W. |
| author_facet | Boyer, Charles P. Huang, Hongnian Legendre, Eveline Tønnesen-Friedman, Christina W. |
| contents | We introduce the notions of weighted extremal K{ä}hler twins together with the related notion of extremal Sasaki twins. In the Kähler setting this leads to a generalization of the twinning phenomenon appearing among LeBrun's strongly Hermitian solutions to the Einstein-Maxwell equations on the first Hirzebruch surface \cite{Leb16} to weighted extremal metrics on Hirzebruch surfaces in general. We discover that many twins appear and that this can be viewed in the Sasaki setting as a case where we have more than one extremal ray in the Sasaki cone even when we do not allow changes within the isotopy class. We also study extremal Sasaki twins directly in the Sasaki setting with a main focus on the toric Sasaki case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13502 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twins in K{ä}hler and Sasaki geometry Boyer, Charles P. Huang, Hongnian Legendre, Eveline Tønnesen-Friedman, Christina W. Differential Geometry We introduce the notions of weighted extremal K{ä}hler twins together with the related notion of extremal Sasaki twins. In the Kähler setting this leads to a generalization of the twinning phenomenon appearing among LeBrun's strongly Hermitian solutions to the Einstein-Maxwell equations on the first Hirzebruch surface \cite{Leb16} to weighted extremal metrics on Hirzebruch surfaces in general. We discover that many twins appear and that this can be viewed in the Sasaki setting as a case where we have more than one extremal ray in the Sasaki cone even when we do not allow changes within the isotopy class. We also study extremal Sasaki twins directly in the Sasaki setting with a main focus on the toric Sasaki case. |
| title | Twins in K{ä}hler and Sasaki geometry |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2411.13502 |