Compact quasi‐Einstein manifolds with boundary

Rafael Diógenes and Tiago Gadelha

Mathematische Nachrichten, 2022, vol. 295, issue 9, 1690-1708

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$\mathbb {S}_{+}^{n}$.

Date: 2022
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https://doi.org/10.1002/mana.202000045

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