Einstein deformations of K\"ahler Einstein metrics

Paul-Andi Nagy

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arXiv · 2603.09028

Einstein deformations of K\"ahler Einstein metrics

Paul-Andi Nagy

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Abstract

We study Einstein deformations of negative K\"ahler Einstein metrics. We relate the second order Einstein deformation theory of negative K\"ahler-Einstein metrics to the complex geometry of the underlying K\"ahler manifold. After suitable gauge normalisation we show that the Taylor expansion to order two of an Einstein deformation tangent to $h_1$ in the infinitesimal deformation space is fully determined by $h_1^2$ and the divergence of the Kodaira-Spencer bracket $[h_1,h_1]^c$. This substantially refines and extends recent results of Nagy-Semmelmann which state that Einstein deformations for negative K\"ahler-Einstein metrics are unobstructed to second order.

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Paul-Andi Nagy. 2026-03-09. Einstein deformations of K\"ahler Einstein metrics. https://arxiv.org/abs/2603.09028

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