All quaternion-Kähler manifolds of negative scalar curvature are stable Einstein metrics, hence scalar-curvature rigid, while some positive-curvature examples are not rigid.
: Differential forms on quaternionic K¨ ahler manifolds, Handbook of pseudo-Riemannian geometry and supersymmetry, 15-37, IRMA Lect
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On stability and scalar curvature rigidity of quaternion-K\"ahler manifolds
All quaternion-Kähler manifolds of negative scalar curvature are stable Einstein metrics, hence scalar-curvature rigid, while some positive-curvature examples are not rigid.