Gravitational Instantons, Weyl Curvature, and Conformally Kähler Geometry - Sorbonne Université
Article Dans Une Revue International Mathematics Research Notices Année : 2024

Gravitational Instantons, Weyl Curvature, and Conformally Kähler Geometry

Résumé

In a previous paper [7], the first two authors classified complete Ricci-flat ALF Riemannian 4-manifolds that are toric and Hermitian, but non-Kähler. In this article, we consider general Ricci-flat metrics on these spaces that are close to a given such gravitational instanton with respect to a norm that imposes reasonable fall-off conditions at infinity. We prove that any such Ricci-flat perturbation is necessarily Hermitian and carries a bounded, non-trivial Killing vector field. With mild additional hypotheses, we are then able to show that the new Ricci-flat metric must actually be one of the known gravitational instantons classified in [7].

Dates et versions

hal-04707548 , version 1 (24-09-2024)

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Olivier Biquard, Paul Gauduchon, Claude Lebrun. Gravitational Instantons, Weyl Curvature, and Conformally Kähler Geometry. International Mathematics Research Notices, 2024, ⟨10.1093/imrn/rnae200⟩. ⟨hal-04707548⟩
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