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math.DG2026
Infinitesimal rigidity of Hermitian gravitational instantons
Lars Andersson, Bernardo Araneda
We prove infinitesimal rigidity and integrability of the moduli space for Hermitian gravitational instantons. Together with the recent proof by Biquard, Gauduchon, and LeBrun of lo…
math.DG2025
All toric Hermitian ALE gravitational instantons
Bernardo Araneda, James Lucietti
We prove that the only smooth, Ricci flat, ALE gravitational instanton with a toric Hermitian non-Kähler structure is the Eguchi-Hanson instanton. The proof is analogous to the cla…
math.DG2023
Hyper-Kähler instantons, symmetries, and flat spaces
Bernardo Araneda
We find all hyper-Kähler 4-manifolds admitting conformal Kähler structures with respect to either orientation, and we show that these structures can be expressed as a combination o…