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arXiv · 2110.13176

Critical metrics on $4$-manifolds with harmonic anti-self dual Weyl tensor

Emanuel Viana
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Abstract

We prove that a $4$-dimensional simply connected, compact critical metric of the volume functional with harmonic anti-self dual Weyl tensor and boundary isometric to a standard sphere $\mathbb{S}^{3}$ is isometric to a geodesic ball in a simply connected space form $\mathbb{R}^{4}$, $\mathbb{H}^{4}$ or $\mathbb{S}^{4}.$

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Emanuel Viana. 2021-10-25. Critical metrics on $4$-manifolds with harmonic anti-self dual Weyl tensor. https://doi.org/10.1016/j.geomphys.2021.104434

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