Instability of conformally Kähler, Einstein metrics

Published 16 Oct 2023 in math.DG | (2310.10109v3)

Abstract: 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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