On the stability of Einstein metrics carrying a special twisted spinor
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909937922211840 |
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| author | Artacho, Diego |
| author_facet | Artacho, Diego |
| contents | We prove linear semi-stability for a large class of Einstein metrics of non-positive scalar curvature. More precisely, we show that any Einstein $n$-manifold with non-positive scalar curvature carrying a parallel twisted pure spin$^r$ spinor is linearly semi-stable, under mild restrictions on $n$ and $r$. We thus extend the parallel spin and spin$^c$ stability results of Dai--Wang--Wei. As an application, our result implies linear semi-stability for all negative quaternion-K{ä}hler manifolds of dimension greater than $8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01620 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the stability of Einstein metrics carrying a special twisted spinor Artacho, Diego Differential Geometry 53C25, 53C27 We prove linear semi-stability for a large class of Einstein metrics of non-positive scalar curvature. More precisely, we show that any Einstein $n$-manifold with non-positive scalar curvature carrying a parallel twisted pure spin$^r$ spinor is linearly semi-stable, under mild restrictions on $n$ and $r$. We thus extend the parallel spin and spin$^c$ stability results of Dai--Wang--Wei. As an application, our result implies linear semi-stability for all negative quaternion-K{ä}hler manifolds of dimension greater than $8$. |
| title | On the stability of Einstein metrics carrying a special twisted spinor |
| topic | Differential Geometry 53C25, 53C27 |
| url | https://arxiv.org/abs/2512.01620 |