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arXiv · 2303.08025

Uniqueness of critical metrics for a quadratic curvature functional

Giovanni Catino·Paolo Mastrolia·Dario D. Monticelli
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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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Giovanni Catino, Paolo Mastrolia, Dario D. Monticelli. 2023-03-14. Uniqueness of critical metrics for a quadratic curvature functional. https://arxiv.org/abs/2303.08025

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