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Critical metrics of the scalar curvature functional satisfying a vanishing condition on the Weyl tensor

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Abstract

It was conjectured in the 80s that every critical metric of the total scalar curvature functional restricted to space of metrics with constant scalar curvature of unitary volume must be Einstein. We prove that such a conjecture is true under a second-order vanishing condition on the Weyl tensor.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Piauí - UFPI, Campus Helvídio Nunes, Picos, PI, CEP 64600-000, Brazil

    Alex Sandro Santos

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  1. Alex Sandro Santos
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Correspondence to Alex Sandro Santos.

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A. Santos was partially supported by CAPES/ Brazil.

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Santos, A.S. Critical metrics of the scalar curvature functional satisfying a vanishing condition on the Weyl tensor. Arch. Math. 109, 91–100 (2017). https://doi.org/10.1007/s00013-017-1030-7

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  • DOI: https://doi.org/10.1007/s00013-017-1030-7

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