Rigidity of critical metrics for quadratic curvature functions on closed Riemannian manifolds
Volume 169 / 2022
Colloquium Mathematicum 169 (2022), 103-116
MSC: Primary 53C24, Secondary 53C21.
DOI: 10.4064/cm8236-6-2021
Published online: 31 January 2022
Abstract
We study rigidity of critical metrics for quadratic curvature functions $\mathcal {F}_{t,s}(g)$ involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor. In particular, when $s=0$, we give new characterizations by pointwise inequalities involving the Weyl curvature and the traceless Ricci tensor for critical metrics with divergence-free Cotton tensor. We also provide a few rigidity results for locally conformally flat critical metrics.
