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

DOI10.1016/j.na.2018.05.017zbMath1395.53054arXiv1802.04454OpenAlexW2963841328WikidataQ125925104 ScholiaQ125925104MaRDI QIDQ1654015

Bingqing Ma, Yu Chen, Guangyue Huang, Xing Xiao Li

Publication date: 7 August 2018

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.04454

zbMATH Keywords

EinsteinrigidityYamabe invariantcritical metric

Mathematics Subject Classification ID

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

Related Items

Rigidity of critical metrics for quadratic curvature functions on closed Riemannian manifolds ⋮ Variational formulae of some functionals by the modified Schouten tensor ⋮ Unnamed Item ⋮ RIGIDITY OF COMPLETE RIEMANNIAN MANIFOLDS WITH VANISHING BACH TENSOR ⋮ Rigidity of Riemannian manifolds with vanishing generalized Bach tensor ⋮ Some rigidity characterizations on critical metrics for quadratic curvature functionals ⋮ Rigidity of Einstein metrics as critical points of some quadratic curvature functionals on complete manifolds ⋮ Some rigidity characterizations of Einstein metrics as critical points for quadratic curvature functionals

Cites Work

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• Rigidity theorem for integral pinched shrinking Ricci solitons
• Einstein manifolds with finite \(L^p\)-norm of the Weyl curvature
• Einstein manifolds
• Critical metrics of the $L^{2}$-norm of the scalar curvature
• Some characterizations on critical metrics for quadratic curvature functions
• A new variational characterization of 𝑛-dimensional space forms
• A new variational characterization of three-dimensional space forms

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