Critical point equation and closed conformal vector fields |
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| Authors: | J. F. da Silva Filho |
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| Affiliation: | Universidade da Integração Internacional da Lusofonia Afro-Brasileira – Unilab, Instituto de Ciências Exatas e da Natureza, Campus das Auroras, Rua José Franco de Oliveira, Redenção/CE, 62.790-970 Brazil |
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| Abstract: | In this article, we study the critical points of the total scalar curvature functional restricted to the space of metrics with constant scalar curvature of unitary volume, for simplicity, CPE metrics. Here, we prove that a CPE metric admitting a non-trivial closed conformal vector field must be isometric to a round sphere metric, which provides a partial answer to the CPE conjecture. |
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| Keywords: | closed conformal vector field critical point equation total scalar curvature functional |
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