Some characterizations on critical metrics for quadratic curvature functions

DOI10.1090/proc/13740zbMath1382.58011OpenAlexW2600472708MaRDI QIDQ4590992

Guangyue Huang, Li Chen

Publication date: 21 November 2017

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13740

zbMATH Keywords

Einsteinquadratic functionalscritical metricspace of Riemannian metricscurvature functionals

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Critical metrics (58E11) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Manifolds of metrics (especially Riemannian) (58D17)

Related Items (7)

Rigidity of Einstein metrics as critical points of quadratic curvature functionals on closed manifolds ⋮ Rigidity of critical metrics for quadratic curvature functions on closed Riemannian manifolds ⋮ Critical metrics for quadratic curvature functionals on some solvmanifolds ⋮ A note on rigidity of Riemannian manifolds with positive scalar curvature ⋮ Rigidity of Riemannian manifolds with vanishing generalized Bach tensor ⋮ Some rigidity characterizations on critical metrics for quadratic curvature functionals ⋮ Some rigidity characterizations of Einstein metrics as critical points for quadratic curvature functionals

Cites Work

• Unnamed Item
• Unnamed Item
• The classification of \((m, \rho)\)-quasi-Einstein manifolds
• Critical metrics of the Schouten functional
• Some rigidity results on critical metrics for quadratic functionals
• Ricci deformation of the metric on a Riemannian manifold
• Effective \(L_p\) pinching for the concircular curvature
• On compact Riemannian manifolds with harmonic curvature
• Deformations of Riemannian metrics on 3-dimensional manifolds
• Extrema of curvature functional on the space of metrics on 3-manifolds
• A note on curvature of Riemannian manifolds
• Rigidity and stability of Einstein metrics for quadratic curvature functionals
• Spaces of Riemannian metrics
• Einstein manifolds
• Sur la réductibilité d'un espace de Riemann
• On conformally flat manifolds with constant positive scalar curvature
• Riemannian manifolds with harmonic curvature
• Campesino a Campesino: Voices from Latin America's Farmer to Farmer Movement for Sustainable Agriculture - By Eric Holt-Gimenez
• Unique continuation in geometry
• Hypersurfaces and a Pinching Problem on the Second Fundamental Tensor
• A critical metric for the 𝐿²-norm of the curvature tensor on 𝑆³
• A new variational characterization of 𝑛-dimensional space forms
• Quelques formules de variation pour une structure riemannienne
• A new variational characterization of three-dimensional space forms

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