Uniqueness of critical metrics for a quadratic curvature functional

Giovanni Catino; Paolo Mastrolia; Dario D. Monticelli

Uniqueness of critical metrics for a quadratic curvature functional

Differential Geometry 2025-01-10 v2

Authors: Giovanni Catino , Paolo Mastrolia , Dario D. Monticelli

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 $n\geq 10$ .

Keywords

critical metrics quadratic curvature functional scalar flat finite energy rigidity non-compact manifolds

Cite

@article{arxiv.2303.08025,
  title  = {Uniqueness of critical metrics for a quadratic curvature functional},
  author = {Giovanni Catino and Paolo Mastrolia and Dario D. Monticelli},
  journal= {arXiv preprint arXiv:2303.08025},
  year   = {2025}
}

Comments

We removed the second result

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