2025/03/31 by Andersson, Lars, Araneda, Bernardo · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.2503.24265
The main result of this paper is that infinitesimal rigidity of the moduli space for Hermitian gravitational instantons holds. An important step in the proof is to show that, provided certain boundary conditions hold, a curve of Riemannian metrics passing through a Hermitian non-Kähler Einstein metric is conformally Kähler to second perturbative order. This uses ideas of Wu and LeBrun. Hermitian non-Kähler Einstein 4-manifolds have a quasi-locally conserved charge, which is shown to correspond to a parameter of the moduli space. This charge is evaluated for all explicitly known examples. It follows from the proof of our main theorem that infinitesimal Einstein deformations admit a closed 2-form that measures the perturbation in the moduli parameter.