Instability of conformally K\"ahler, Einstein metrics

Olivier Biquard; Tristan Ozuch

Instability of conformally K\"ahler, Einstein metrics

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arxiv 2310.10109 v3 pith:AQIDTQCT submitted 2023-10-16 math.DG

Olivier Biquard , Tristan Ozuch This is my paper · ORCID

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keywords ahlerconformallyeinsteininstabilityapplieschen-lebrun-webercompactcurvature

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We prove the instability of conformally K\"ahler, compact or ALF Einstein 4-manifolds with nonnegative scalar curvature which are not half conformally flat. This applies to all the known examples of gravitational instantons which are not hyperK\"ahler and to the Chen-Lebrun-Weber metric in particular.

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Einstein metrics, their moduli spaces and stability
math.DG 2025-07 conditional novelty 2.0 of 10

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.

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