Some rigidity characterizations of Einstein metrics as critical points for quadratic curvature functionals

Abstract

We study rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor, characterized by some pointwise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moreover, we also provide a few rigidity results for locally conformally flat critical metrics.

All comments are welcome

References in corpus (2)

• On Bach-flat gradient shrinking Ricci solitons
• Rigidity of complete Riemannian manifolds with vanishing Bach tensor