Critical point equation on four‐dimensional compact manifolds | Zendy

Barros Abdênago | Zendy; Ribeiro Ernani | Zendy

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Critical point equation on four‐dimensional compact manifolds

Author(s) -

Barros Abdênago,

Ribeiro Ernani

Publication year - 2014

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.201300149

Subject(s) - mathematics , scalar curvature , focus (optics) , mathematical analysis , metric (unit) , constant (computer programming) , critical point (mathematics) , curvature , scalar (mathematics) , point (geometry) , space (punctuation) , pure mathematics , geometry , physics , operations management , computer science , optics , economics , programming language , linguistics , philosophy

The aim of this article is to study the space of metrics with constant scalar curvature of volume 1 that satisfies the critical point equationL g * ( f ) = R i c ˚ , for simplicity CPE metrics. It has been conjectured that every CPE metric must be Einstein. Here, we shall focus our attention for 4‐dimensional half conformally flat manifolds M 4 . In fact, we shall show that for a nontrivial f ,M 4must be isometric to a sphereS 4 and f is some height function onS 4 .

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