Codice QDD197 Titolo Critical metrics of the $L^2$-norm of the scalar curvature Data 2015-02-26 Autore/i Catino, G. Link Download full text Pubblicato Proc. Amer. Math. Soc.,142 (2014), 3981-3986 Abstract 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.