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Survey explores hyperkähler and Hermitian gravitational instantons, indicating future research directions.
We survey recent progress in the classification of hyperkähler and Hermitian gravitational instantons (i.e., complete noncompact four dimensional Ricci-flat manifolds with quadratic curvature decay), as well as the construction of non-Hermitian gravitational instantons via harmonic maps. We also present a list of open questions related to gravitational instantons.
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Li et al. (2026) studied this question.
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