Kählerity of Einstein four-manifolds
Li, Xiaolong Zhang, Yongjia
Li, Xiaolong
Zhang, Yongjia
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2024
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Article
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53C21,53C25,53C55,Curvature restriction,Einstein four-manifolds,Kähler–Einstein,Self-dual Weyl tensor
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Li, X., Zhang, Y. Kählerity of Einstein four-manifolds. (2024). Mathematische Zeitschrift, 307 (1), art. no. 4. DOI: 10.1007/s00209-024-03480-1
Abstract
We prove that a closed oriented Einstein four-manifold is either anti-self-dual or (after passing to a double Riemannian cover if necessary) Kähler–Einstein, provided that λ2≥-S12, where λ2 is the middle eigenvalue of the self-dual Weyl tensor W+ and S is the scalar curvature. An analogous result holds for closed oriented four-manifolds with δW+=0. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
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Springer Science and Business Media Deutschland GmbH
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Mathematische Zeitschrift
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0025-5874