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arXiv · 2412.13351

On stability and scalar curvature rigidity of quaternion-K\"ahler manifolds

Klaus Kroencke·Uwe Semmelmann
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Abstract

We show that every quaternion-K\"ahler 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-K\"ahler manifolds of positive scalar curvature which are not scalar curvature rigid even though they are semi-stable.

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Klaus Kroencke, Uwe Semmelmann. 2024-12-17. On stability and scalar curvature rigidity of quaternion-K\"ahler manifolds. https://arxiv.org/abs/2412.13351

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