Classification of 4-dimensional homogeneous weakly einstein manifolds

DOI10.1007/s10587-015-0159-4zbMath1363.53032OpenAlexW2086472757MaRDI QIDQ5249646

Teresa Arias-Marco, Oldřich Kowalski

Publication date: 6 May 2015

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10338.dmlcz/144212

zbMATH Keywords

Einstein manifoldRiemannian homogeneous manifoldweakly Einstein manifold

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Methods of local Riemannian geometry (53B21)

Related Items (11)

Four-Dimensional Homogeneous Generalizations of Einstein Metrics ⋮ Unnamed Item ⋮ Invariant metrics on Lie groups ⋮ Weakly Einstein real hypersurfaces in \(\mathbb{C} P^2\) and \(\mathbb{C} H^2\) ⋮ 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 ⋮ Structure of locally conformally flat manifolds satisfying some weakly-Einstein conditions ⋮ Conformally Einstein and Bach-flat four-dimensional homogeneous manifolds ⋮ Locally conformally flat weakly-Einstein manifolds ⋮ Six-dimensional Lie-Einstein metrics ⋮ Weakly Einstein critical metrics of the volume functional on compact manifolds with boundary

Uses Software

• Mathematica

Cites Work

• Critical metrics for quadratic functionals in the curvature on 4-dimensional manifolds
• Curvatures of left invariant metrics on Lie groups
• A curvature identity on a 4-dimensional Riemannian manifold
• Homogeneous Einstein spaces of dimension four
• A generalization of a 4-dimensional Einstein manifold
• Unit Tangent Sphere Bundles with Constant Scalar Curvature
• Classification of Solvable Lie Algebras
• Classification of 4-dimensional homogeneous D’Atri spaces
• Mean-value theorems for Riemannian manifolds

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