Kählerity of Einstein four-manifolds

2022/06/10 by Xiaolong Li, Yongjia Zhang, Li, Xiaolong +1
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2206.04870

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) Kähler-Einstein, provided that λ₂ ≥ -(S)/(12), where λ₂ 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 δW⁺=0.

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