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Closed three-dimensional vacuum static spaces


This article is devoted to the study of the closed vacuum static spaces. Based on the argument of maximum principle, we show that three-dimensional closed vacuum static spaces with scalar curvature 6 must be isometric to either the standard unit sphere \({\mathbb {S}}^3(1)\) or a finite quotient of the torus \(\mathbb S^1(\sqrt{1/3})\times {\mathbb {S}}^2(\sqrt{1/3}).\)

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The first author was partially supported by the starting-up research funds through Nanjing University with account No. 020314912205. We would like to express our gratitude to the referee for critical comments and valuable suggestions.

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Correspondence to Jian Ye.

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Xu, X., Ye, J. Closed three-dimensional vacuum static spaces. Invent. math. (2022).

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Mathematics Subject Classification

  • 53C21
  • 53C24
  • 53C25