Critical metrics of the total scalar curvature functional on 4‐manifolds |
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| Authors: | A Barros B Leandro E Ribeiro Jr |
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| Institution: | 1. Universidade Federal do Ceará – UFC, Departamento de Matemática, Fortaleza/CE, Brazil;2. Universidade de Brasília – UNB, Departamento de Matemática, Brasília/DF, Brazil |
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| Abstract: | The purpose of this paper is to investigate the critical points of the total scalar curvature functional restricted to space of metrics with constant scalar curvature of unitary volume, for simplicity CPE metrics. It was conjectured in the 1980's that every CPE metric must be Einstein. We prove that a 4‐dimensional CPE metric with harmonic tensor  must be isometric to a round sphere  |
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| Keywords: | Total scalar curvature functional critical point equation Einstein metric Primary: 53C20 53C21 53C25 53C65 |
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