Critical metrics of the $L^2$-norm of the scalar curvature

Giovanni Catino

arxiv: 1204.2744 · v2 · pith:2BXC3DLCnew · submitted 2012-04-12 · 🧮 math.DG · math.AP

Critical metrics of the L²-norm of the scalar curvature

Giovanni Catino This is my paper

classification 🧮 math.DG math.AP

keywords curvaturescalarcriticalmetricscompletenormcharacterizeconstant

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In this paper we investigate complete critical metrics of the $L^{2}$-norm of the scalar curvature. We prove that any complete critical metric with positive scalar curvature has constant scalar curvature and we characterize critical metrics with nonnegative scalar curvature in dimension three and four.

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Critical metrics of the L²-norm of the scalar curvature

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