On the stability of Einstein metrics carrying a special twisted spinor

2025/12/01 by Diego Artacho, Artacho, Diego
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2512.01620

Abstract

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-Kähler manifolds of dimension greater than 8.

Citations

• Some isolation and stability results for Einstein manifolds
• On stability and scalar curvature rigidity of quaternion-Kähler manifolds
• On the Stability of Riemannian Manifold with Parallel Spinors

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