Bott-Chern formality and Massey products on strong Kähler with torsion and Kähler solvmanifolds
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913229424295936 |
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| author | Sferruzza, Tommaso Tomassini, Adriano |
| author_facet | Sferruzza, Tommaso Tomassini, Adriano |
| contents | We study the interplay between geometrically-Bott-Chern-formal metrics and SKT metrics. We prove that a $6$-dimensional nilmanifold endowed with a invariant complex structure admits an SKT metric if and only if it is geometrically-Bott-Chern-formal. We also provide some partial results in higher dimensions for nilmanifolds endowed with a class of suitable complex structures. Furthermore, we prove that any Kähler solvmanifold is geometrically formal. Finally, we explicitly construct lattices for a complex solvable Lie group in the list of Nakamura [23] on which we provide a non vanishing quadruple $ABC$-Massey product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02537 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bott-Chern formality and Massey products on strong Kähler with torsion and Kähler solvmanifolds Sferruzza, Tommaso Tomassini, Adriano Differential Geometry 53C55 (Primary) 53B35, 22E25 (Secondary) We study the interplay between geometrically-Bott-Chern-formal metrics and SKT metrics. We prove that a $6$-dimensional nilmanifold endowed with a invariant complex structure admits an SKT metric if and only if it is geometrically-Bott-Chern-formal. We also provide some partial results in higher dimensions for nilmanifolds endowed with a class of suitable complex structures. Furthermore, we prove that any Kähler solvmanifold is geometrically formal. Finally, we explicitly construct lattices for a complex solvable Lie group in the list of Nakamura [23] on which we provide a non vanishing quadruple $ABC$-Massey product. |
| title | Bott-Chern formality and Massey products on strong Kähler with torsion and Kähler solvmanifolds |
| topic | Differential Geometry 53C55 (Primary) 53B35, 22E25 (Secondary) |
| url | https://arxiv.org/abs/2402.02537 |