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Compact quasi‐Einstein manifolds with boundary

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  • Rafael Diógenes
  • Tiago Gadelha

Abstract

The goal of this article is to study compact quasi‐Einstein manifolds with boundary. We provide boundary estimates for compact quasi‐Einstein manifolds similar to previous results obtained for static and V‐static spaces. In addition, we show that compact quasi‐Einstein manifolds with connected boundary and satisfying a suitable pinching condition must be isometric, up to scaling, to the standard hemisphere S+n$\mathbb {S}_{+}^{n}$.

Suggested Citation

  • Rafael Diógenes & Tiago Gadelha, 2022. "Compact quasi‐Einstein manifolds with boundary," Mathematische Nachrichten, Wiley Blackwell, vol. 295(9), pages 1690-1708, September.
    • Handle: RePEc:bla:mathna:v:295:y:2022:i:9:p:1690-1708
    DOI: 10.1002/mana.202000045
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    References listed on IDEAS

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    1. A. Barros & A. da Silva, 2019. "Rigidity for critical metrics of the volume functional," Mathematische Nachrichten, Wiley Blackwell, vol. 292(4), pages 709-719, April.
    2. Ernani Ribeiro Jr & Keti Tenenblat, 2021. "Noncompact quasi‐Einstein manifolds conformal to a Euclidean space," Mathematische Nachrichten, Wiley Blackwell, vol. 294(1), pages 132-144, January.
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