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

Emanuel Viana

doi:10.1016/j.geomphys.2021.104434

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

Differential Geometry 2022-01-19 v3

Authors: 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 $\mathbb{S}^{4}.$

Keywords

critical metrics volume functional weyl tensor 4-manifolds space forms differential geometry

Cite

@article{arxiv.2110.13176,
  title  = {Critical metrics on $4$-manifolds with harmonic anti-self dual Weyl tensor},
  author = {Emanuel Viana},
  journal= {arXiv preprint arXiv:2110.13176},
  year   = {2022}
}

Comments

Fixed typos

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