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Critical metrics of the total scalar curvature functional on 4‐manifolds
Author(s) -
Barros A.,
Leandro B.,
Ribeiro E.
Publication year - 2015
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.201400390
Subject(s) - scalar curvature , mathematics , curvature , ricci curvature , scalar (mathematics) , metric (unit) , riemann curvature tensor , pure mathematics , mathematical analysis , prescribed scalar curvature problem , unitary state , constant (computer programming) , mathematical physics , sectional curvature , geometry , computer science , operations management , political science , law , economics , programming language
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 W + must be isometric to a round sphereS 4 .