Holomorphically parallelizable solvmanifolds with special metrics and their deformations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909014583934976 |
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| author | Giudice, Ettore Lo Rubini, Lapo Tomassini, Adriano |
| author_facet | Giudice, Ettore Lo Rubini, Lapo Tomassini, Adriano |
| contents | We investigate the existence of strong Kähler with torsion metrics along deformations of the Iwasawa manifold and of the holomorphically parallelizable Nakamura manifold. We also show that the class of deformations of the holomorphically parallelizable Nakamura manifold yielding a non-left-invariant complex structure admits a balanced metric but does not admit any strong Kähler with torsion metric. We then construct the Kuranishi space of a $4$-dimensional holomorphically parallelizable solvmanifold and study whether small deformations of such a manifold admit SKT metrics. Finally, we provide some results concerning the existence of metrics satisfying $\partial \bar{\partial} ω= 0$, $\partial \bar{\partial} ω^2 = 0$ on a particular class of $2$-step nilpotent nilmanifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03852 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Holomorphically parallelizable solvmanifolds with special metrics and their deformations Giudice, Ettore Lo Rubini, Lapo Tomassini, Adriano Differential Geometry 53C15, 32G05 We investigate the existence of strong Kähler with torsion metrics along deformations of the Iwasawa manifold and of the holomorphically parallelizable Nakamura manifold. We also show that the class of deformations of the holomorphically parallelizable Nakamura manifold yielding a non-left-invariant complex structure admits a balanced metric but does not admit any strong Kähler with torsion metric. We then construct the Kuranishi space of a $4$-dimensional holomorphically parallelizable solvmanifold and study whether small deformations of such a manifold admit SKT metrics. Finally, we provide some results concerning the existence of metrics satisfying $\partial \bar{\partial} ω= 0$, $\partial \bar{\partial} ω^2 = 0$ on a particular class of $2$-step nilpotent nilmanifolds. |
| title | Holomorphically parallelizable solvmanifolds with special metrics and their deformations |
| topic | Differential Geometry 53C15, 32G05 |
| url | https://arxiv.org/abs/2605.03852 |