A survey showing that stability and infinitesimal deformability of Einstein metrics both reduce to the spectrum of the Lichnerowicz Laplacian, with a compendium of known results and open questions.
Some isolation and stability results for Einstein manifolds
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abstract
We prove new isolation and stability results for Einstein manifolds in a variety of settings. Imposing conditions on the Weyl tensor, we establish new stability criteria for compact, asymptotically hyperbolic (AH) and asymptotically locally Euclidean (ALE) manifolds and an isolation result in the latter setting. For compact K\"ahler and Sasaki $\eta$-Einstein manifolds, we provide similar results which involve the Bochner tensor and the contact Bochner tensor, respectively.
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Einstein metrics, their moduli spaces and stability
A survey showing that stability and infinitesimal deformability of Einstein metrics both reduce to the spectrum of the Lichnerowicz Laplacian, with a compendium of known results and open questions.