Normal homogeneous spaces are a natural setting in which Casimir operators occur. In the 80s, Koiso studied the stability of symmetric spaces of compact type, utilizing the coincidence of ΔL with a Casimir operator. Motivated by his and also the G-stability results of Lauret-Lauret-Will, we generalize Koiso's strategy to general normal homogeneous spaces.
Ultimately this approach is sufficient to provide many new non-symmetric examples of stable Einstein manifolds of positive scalar curvature.
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