Rigidity results for non-Kähler Calabi-Yau geometries on threefolds
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911366514737152 |
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| author | Apostolov, Vestislav Barbaro, Giuseppe Lee, Kuan-Hui Streets, Jeffrey |
| author_facet | Apostolov, Vestislav Barbaro, Giuseppe Lee, Kuan-Hui Streets, Jeffrey |
| contents | We derive a canonical symmetry reduction associated to a compact non-Kähler Bismut-Hermitian-Einstein manifold. In real dimension $6$, the transverse geometry is conformally Kähler, and we give a complete description in terms of a single scalar PDE for the underlying Kähler structure. In the case when the soliton potential is constant, we show that that the Bott-Chern number $h^{1,1}_{BC} \geq 2$, and that equality holds if and only if the metric is Bismut-flat, and hence a quotient of either $\SU(2) \times \mathbb R \times \mathbb C$ or $\SU(2) \times \SU(2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigidity results for non-Kähler Calabi-Yau geometries on threefolds Apostolov, Vestislav Barbaro, Giuseppe Lee, Kuan-Hui Streets, Jeffrey Differential Geometry We derive a canonical symmetry reduction associated to a compact non-Kähler Bismut-Hermitian-Einstein manifold. In real dimension $6$, the transverse geometry is conformally Kähler, and we give a complete description in terms of a single scalar PDE for the underlying Kähler structure. In the case when the soliton potential is constant, we show that that the Bott-Chern number $h^{1,1}_{BC} \geq 2$, and that equality holds if and only if the metric is Bismut-flat, and hence a quotient of either $\SU(2) \times \mathbb R \times \mathbb C$ or $\SU(2) \times \SU(2)$. |
| title | Rigidity results for non-Kähler Calabi-Yau geometries on threefolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2408.09648 |