Rigidity of Einstein metrics as critical points of some quadratic curvature functionals on complete manifolds

DOI10.1007/s12220-020-00563-3zbMath1477.53075arXiv1804.10748OpenAlexW3118430685MaRDI QIDQ2050610

Yu Chen, Guangyue Huang, Xing Xiao Li

Publication date: 31 August 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.10748

zbMATH Keywords

rigidityEinstein metricSobolev constantcritical metric

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Rigidity results (53C24)

Related Items (2)

Critical metrics for quadratic curvature functionals on some solvmanifolds ⋮ Rigidity of Riemannian manifolds with vanishing generalized Bach tensor

Cites Work

• A variational characterization of flat spaces in dimension three
• Integral pinched shrinking Ricci solitons
• Some rigidity results on critical metrics for quadratic functionals
• Ricci deformation of the metric on a Riemannian manifold
• Conformally flat manifolds, Kleinian groups and scalar curvature
• Effective \(L_p\) pinching for the concircular curvature
• Refined Kato inequalities and conformal weights in Riemannian geometry
• Rigidity of Einstein metrics as critical points of quadratic curvature functionals on closed manifolds
• Rigidity theorems for compact Bach-flat manifolds with positive constant scalar curvature
• Rigidity of Riemannian manifolds with positive scalar curvature
• Some remarks on Riemannian manifolds with parallel Cotton tensor
• Rigidity theorem for integral pinched shrinking Ricci solitons
• Einstein manifolds with finite \(L^p\)-norm of the Weyl curvature
• Rigidity of complete manifolds with parallel Cotton tensor
• Integral pinched gradient shrinking \(\rho\)-Einstein solitons
• Einstein manifolds
• Critical metrics of the $L^{2}$-norm of the scalar curvature
• Some remarks on Bach-flat manifolds with positive constant scalar curvature
• Extrema of curvature functionals on the space of metrics on 3-manifolds. II
• Unnamed Item

This page was built for publication: Rigidity of Einstein metrics as critical points of some quadratic curvature functionals on complete manifolds