Submitted Paper

Inserted: 14 mar 2023
Last Updated: 9 jan 2025

Year: 2023

Abstract:

In this paper we prove a new rigidity results for complete, possibly non-compact, critical metrics of the quadratic curvature functional $\mathfrak{S}^2 = \int R_g^{2} dV_g$: we show that critical metrics $(M^n, g)$ with finite energy are always scalar flat, i.e. global minima, provided $n\geq 10$.

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