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arXiv · 2206.04870

K\"ahlerity of Einstein four-manifolds

Xiaolong Li·Yongjia Zhang
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Abstract

We prove that a closed oriented Einstein four-manifold is either anti-self-dual or (after passing to a double Riemann cover if necessary) K\"ahler-Einstein, provided that $\lambda_2 \geq -\frac{S}{12}$, where $\lambda_2$ is the middle eigenvalue of the self-dual Weyl tensor $W^+$ and $S$ is the scalar curvature. The same conclusion holds for closed oriented four-manifolds with $\delta W^+=0$.

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Xiaolong Li, Yongjia Zhang. 2022-06-10. K\"ahlerity of Einstein four-manifolds. https://arxiv.org/abs/2206.04870

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