Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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G. Catino - P. Mastrolia - Dario D. Monticelli

Uniqueness of critical metrics for a quadratic curvature functional

created by catino on 17 Oct 2023



Inserted: 17 oct 2023
Last Updated: 17 oct 2023

Year: 2023

ArXiv: 2303.08025 PDF


In this paper we prove new rigidity results for complete, possibly non-compact, critical metrics of the quadratic curvature functionals $\mathfrak{S}^2 = \int R_g^{2} dV_g$. 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.

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