Critical metrics for quadratic functionals in the curvature on 4-dimensional manifolds

DOI10.1016/J.DIFGEO.2011.07.001zbMath1228.58010OpenAlexW2013933468WikidataQ115356812 ScholiaQ115356812MaRDI QIDQ719860

Kouei Sekigawa, Yunhee Euh, Jeong Hyeong Park

Publication date: 12 October 2011

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2011.07.001

zbMATH Keywords

curvature tensorscalar curvatureRicci tensorcritical metric

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Critical metrics (58E11) Manifolds of metrics (especially Riemannian) (58D17)

Related Items (17)

Singer-Thorpe bases for special Einstein curvature tensors in dimension 4 ⋮ Curvature identities derived from the integral formula for the first Pontrjagin number ⋮ Transplanting geometrical structures ⋮ Weakly Einstein real hypersurfaces in \(\mathbb{C} P^2\) and \(\mathbb{C} H^2\) ⋮ Critical metrics for quadratic curvature functionals on some solvmanifolds ⋮ Curvature identities for Einstein manifolds of dimensions 5 and 6 ⋮ Weakly-Einstein conditions over locally conformally flat Lorentzian three-manifolds ⋮ A curvature identity on a 4-dimensional Riemannian manifold ⋮ Strongly Einstein real hypersurfaces in \(\mathbb{C}P^2\) and \(\mathbb{C}H^2\) ⋮ Three-dimensional homogeneous contact metric manifold with weakly $\eta$-Einstein structures ⋮ Universal curvature identities ⋮ Four-dimensional homogeneous manifolds satisfying some Einstein-like conditions ⋮ Locally conformally flat weakly-Einstein manifolds ⋮ Weakly Einstein critical metrics of the volume functional on compact manifolds with boundary ⋮ Classification of 4-dimensional homogeneous weakly einstein manifolds ⋮ Critical metrics for all quadratic curvature functionals ⋮ Critical metrics and massive gravity solutions on three-dimensional Brinkmann waves*

Cites Work

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• Variational properties of the Gauss-Bonnet curvatures
• Some generalizations of the Riemann spaces of Einstein
• Curvature and critical Riemannian metric
• A curvature identity on a 4-dimensional Riemannian manifold
• Einstein manifolds
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• A generalization of a 4-dimensional Einstein manifold
• LOCALLY HOMOGENEOUS CRITICAL METRICS ON FOUR-DIMENSIONAL MANIFOLDS
• Quelques formules de variation pour une structure riemannienne

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