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Remarks on critical point metrics of the total scalar curvature functional

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Abstract

The aim of this short note is to study the space of metrics with constant scalar curvature satisfying the critical point equation on compact manifolds, for simplicity, CPE metrics. It has been conjectured that every CPE metric must be Einstein. Here, we prove that a CPE metric must be isometric to a round sphere under suitable integral conditions inherited from the standard sphere.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, CE, 60455-760, Brazil

    F. Benjamim Filho

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  1. F. Benjamim Filho
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Correspondence to F. Benjamim Filho.

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Partially supported by CNPq/Brazil.

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Filho, F.B. Remarks on critical point metrics of the total scalar curvature functional. Arch. Math. 104, 463–470 (2015). https://doi.org/10.1007/s00013-015-0761-6

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  • DOI: https://doi.org/10.1007/s00013-015-0761-6

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