On stability and scalar curvature rigidity of quaternion-Kähler manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915069386817536 |
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| author | Kroencke, Klaus Semmelmann, Uwe |
| author_facet | Kroencke, Klaus Semmelmann, Uwe |
| contents | We show that every quaternion-Kähler manifold of negative scalar curvature is stable as an Einstein manifold and therefore scalar curvature rigid. In particular, this implies that every irreducible nonpositive Einstein manifold of special holonomy is stable. In contrast, we demonstrate that there exist quaternion-Kähler manifolds of positive scalar curvature which are not scalar curvature rigid even though they are semi-stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13351 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On stability and scalar curvature rigidity of quaternion-Kähler manifolds Kroencke, Klaus Semmelmann, Uwe Differential Geometry 53C25, 53C26, 58J50 We show that every quaternion-Kähler manifold of negative scalar curvature is stable as an Einstein manifold and therefore scalar curvature rigid. In particular, this implies that every irreducible nonpositive Einstein manifold of special holonomy is stable. In contrast, we demonstrate that there exist quaternion-Kähler manifolds of positive scalar curvature which are not scalar curvature rigid even though they are semi-stable. |
| title | On stability and scalar curvature rigidity of quaternion-Kähler manifolds |
| topic | Differential Geometry 53C25, 53C26, 58J50 |
| url | https://arxiv.org/abs/2412.13351 |