Invariant conformal Killing forms on almost abelian Lie groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911777028046848 |
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| author | Herrera, Cecilia Origlia, Marcos |
| author_facet | Herrera, Cecilia Origlia, Marcos |
| contents | We describe completely conformal Killing or conformal Killing-Yano (CKY) $p$-forms on almost abelian metric Lie algebras. In particular we prove that if a $n$-dimensional almost abelian metric Lie algebra admits a non-parallel CKY $p$-form, then $p=1$ or $p=n-1$. In other words, any CKY $p$-form on a metric almost abelian Lie algebra is parallel for $2\leq p\leq n-2$. Moreover, we characterize almost abelian Lie algebras admitting non-parallel CKY $p$-forms, and we classify all Lie algebras with this property up to dimension $5$, distinguishing also those cases where the associated simply connected Lie group admits lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09229 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariant conformal Killing forms on almost abelian Lie groups Herrera, Cecilia Origlia, Marcos Differential Geometry We describe completely conformal Killing or conformal Killing-Yano (CKY) $p$-forms on almost abelian metric Lie algebras. In particular we prove that if a $n$-dimensional almost abelian metric Lie algebra admits a non-parallel CKY $p$-form, then $p=1$ or $p=n-1$. In other words, any CKY $p$-form on a metric almost abelian Lie algebra is parallel for $2\leq p\leq n-2$. Moreover, we characterize almost abelian Lie algebras admitting non-parallel CKY $p$-forms, and we classify all Lie algebras with this property up to dimension $5$, distinguishing also those cases where the associated simply connected Lie group admits lattices. |
| title | Invariant conformal Killing forms on almost abelian Lie groups |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2402.09229 |