Critical point equation and closed conformal vector fields
Copyright policy )Critical point equation and closed conformal vector fields
AbstractIn 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.
Critical metrics, total scalar curvature functional, CPE metrics, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Global Riemannian geometry, including pinching, closed conformal vector fields
Critical metrics, total scalar curvature functional, CPE metrics, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Global Riemannian geometry, including pinching, closed conformal vector fields
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