On indefinite Einstein solvmanifolds admitting a Killing spinor
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916873732358144 |
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| author | Conti, Diego Rossi, Federico A. Dalmasso, Romeo Segnan |
| author_facet | Conti, Diego Rossi, Federico A. Dalmasso, Romeo Segnan |
| contents | Riemannian Einstein solvmanifolds can be described in terms of nilsolitons, namely nilpotent Lie groups endowed with a left-invariant Ricci soliton metric. This characterization does not extend to indefinite metrics; nonetheless, nilsolitons can be defined and used to construct Einstein solvmanifolds of a higher dimension in any signature.
An Einstein solvmanifold obtained by this construction turns out to satisfy the pseudo-Iwasawa condition, meaning that its Lie algebra splits as the orthogonal sum of a nilpotent ideal and an abelian subalgebra, the latter acting by symmetric derivations.
We prove that the only pseudo-Iwasawa solvmanifolds that admit a Killing spinor, invariant or not, are the hyperbolic half-spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23714 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On indefinite Einstein solvmanifolds admitting a Killing spinor Conti, Diego Rossi, Federico A. Dalmasso, Romeo Segnan Differential Geometry 53C25 (Primary) 53C50, 53C27, 22E25, 53C30 (Secondary) Riemannian Einstein solvmanifolds can be described in terms of nilsolitons, namely nilpotent Lie groups endowed with a left-invariant Ricci soliton metric. This characterization does not extend to indefinite metrics; nonetheless, nilsolitons can be defined and used to construct Einstein solvmanifolds of a higher dimension in any signature. An Einstein solvmanifold obtained by this construction turns out to satisfy the pseudo-Iwasawa condition, meaning that its Lie algebra splits as the orthogonal sum of a nilpotent ideal and an abelian subalgebra, the latter acting by symmetric derivations. We prove that the only pseudo-Iwasawa solvmanifolds that admit a Killing spinor, invariant or not, are the hyperbolic half-spaces. |
| title | On indefinite Einstein solvmanifolds admitting a Killing spinor |
| topic | Differential Geometry 53C25 (Primary) 53C50, 53C27, 22E25, 53C30 (Secondary) |
| url | https://arxiv.org/abs/2507.23714 |