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Critical point equation and closed conformal vector fields
Author(s) -
da Silva Filho J. F.
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900316
Subject(s) - mathematics , conformal map , scalar curvature , curvature , conjecture , scalar (mathematics) , killing vector field , vector field , unitary state , constant curvature , metric (unit) , mathematical analysis , pure mathematics , geometry , operations management , political science , law , economics
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.