Bismut Hermitian Einstein metrics and the stability of the pluriclosed flow
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914960371613696 |
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| author | Barbaro, Giuseppe |
| author_facet | Barbaro, Giuseppe |
| contents | We compute the (1,1)-Aeppli cohomology of compact simply-connected Lie groups. From this, we deduce that the Bismut flat metrics on the compact Bismut flat manifolds with finite fundamental group are globally stable for the pluriclosed flow. This prevents the existence of non-flat homogeneous Bismut Hermitian Einstein (hence also pluriclosed Calabi--Yau with torsion) metrics on C-spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_10207 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bismut Hermitian Einstein metrics and the stability of the pluriclosed flow Barbaro, Giuseppe Differential Geometry Complex Variables We compute the (1,1)-Aeppli cohomology of compact simply-connected Lie groups. From this, we deduce that the Bismut flat metrics on the compact Bismut flat manifolds with finite fundamental group are globally stable for the pluriclosed flow. This prevents the existence of non-flat homogeneous Bismut Hermitian Einstein (hence also pluriclosed Calabi--Yau with torsion) metrics on C-spaces. |
| title | Bismut Hermitian Einstein metrics and the stability of the pluriclosed flow |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2307.10207 |