Critical point equation and closed conformal vector fields

J. F. da Silva Filho

Mathematische Nachrichten, 2020, vol. 293, issue 12, 2299-2305

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.

Date: 2020
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