Uniqueness of critical metrics for a quadratic curvature functional

created by catino on 14 Mar 2023
modified on 22 Mar 2023

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Submitted Paper

Inserted: 14 mar 2023
Last Updated: 22 mar 2023

Year: 2023

Abstract:

In this paper we prove 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. a global minimum, provided $n\geq 10$ or $7\leq n \leq 9$ and $M^n$ has at least two ends.