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A new variational characterization of compact conformally flat 4-manifolds

Faen Wu, Xinnuan Zhao (2012)

Communications in Mathematics

In this paper, we give a new variational characterization of certain 4-manifolds. More precisely, let R and R i c denote the scalar curvature and Ricci curvature respectively of a Riemannian metric, we prove that if ( M 4 , g ) is compact and locally conformally flat and g is the critical point of the functional F ( g ) = M 4 ( a R 2 + b | R i c | 2 ) d v g , where ( a , b ) 2 L 1 L 2 L ...

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