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Critical metrics for quadratic functionals in the curvature on 4-dimensional manifolds. (English) Zbl 1228.58010

Summary: We study critical metrics for the squared \(L^{2}\)-norm functionals of the curvature tensor, the Ricci tensor and the scalar curvature by making use of a curvature identity on 4-dimensional Riemannian manifolds.

MSC:

58E11 Critical metrics
53C20 Global Riemannian geometry, including pinching
58D17 Manifolds of metrics (especially Riemannian)
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