Critical metrics of the Schouten functional

DOI10.1007/s00022-010-0057-8zbMath1208.58015OpenAlexW2032499302MaRDI QIDQ622553

Seiki Nishikawa, Udo Simon, Ze-Jun Hu

Publication date: 3 February 2011

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-010-0057-8

zbMATH Keywords

Schouten tensorconformally flat metricSchouten functionalself-dual metric

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global Riemannian geometry, including pinching (53C20) Critical metrics (58E11) Manifolds of metrics (especially Riemannian) (58D17)

Related Items (8)

Three-dimensional homogeneous critical metrics for quadratic curvature functionals ⋮ Prescribed diagonal Schouten tensor in locally conformally flat manifolds ⋮ Some rigidity results on critical metrics for quadratic functionals ⋮ Some characterizations on critical metrics for quadratic curvature functions ⋮ Bach-flat critical metrics for quadratic curvature functionals ⋮ Prescribed Schouten tensor in locally conformally flat manifolds ⋮ 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

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• The principle of symmetric criticality
• On a conformally invariant functional of the space of Riemannian metrics
• Classification of certain compact Riemannian manifolds with harmonic curvature and non-parallel Ricci tensor
• Curvatures of left invariant metrics on Lie groups
• Extrema of curvature functional on the space of metrics on 3-manifolds
• On critical Riemannian metrics for a curvature functional on 3-manifolds
• A conformally invariant sphere theorem in four dimensions
• Conformal geometry, contact geometry, and the calculus of variations
• Schouten curvature functions on locally conformally flat Riemannian manifolds
• On conformally flat critical Riemannian metrics for a curvature functional
• Curvature operators: pinching estimates and geometric examples
• 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
• Extrema of curvature functionals on the space of metrics on 3-manifolds. II
• A new variational characterization of three-dimensional space forms

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