Three-dimensional Riemannian manifolds with constant principal Ricci curvatures ρ1=ρ2≠ρ3

DOI10.1063/1.531626zbMath0866.53026OpenAlexW2060626566WikidataQ115329196 ScholiaQ115329196MaRDI QIDQ5284843

Peter Bueken

Publication date: 20 July 1997

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531626

zbMATH Keywords

local classificationcurvature homogeneous spaces

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Global Riemannian geometry, including pinching (53C20)

Related Items (14)

Riemannian manifolds whose curvature operator R(X, Y) has constant eigenvalues ⋮ Curvature homogeneous critical metrics in dimension three ⋮ On curvature homogeneous three-dimensional Lorentzian manifolds ⋮ On some structure results for Gödel-type spacetimes ⋮ Existence and classification of three-dimensional Lorentzian manifolds with prescribed distinct Ricci eigenvalues ⋮ Riemannian 3-metrics with a generic Codazzi Ricci tensor ⋮ Three-dimensional Lorentzian manifolds with constant principal Ricci curvatures ρ1=ρ2≠ρ3 ⋮ Pseudo-Riemannian 3-manifolds with prescribed distinct constant Ricci eigenvalues ⋮ Three-dimensional homogeneous Lorentzian metrics with prescribed Ricci tensor ⋮ Unit Tangent Sphere Bundles with Constant Scalar Curvature ⋮ Three-dimensional Ivanov–Petrova manifolds ⋮ Hypersurfaces with a parallel higher fundamental form ⋮ Three-dimensional metrics with a spherical homogeneous model ⋮ PSEUDO-SYMMETRIC LORENTZIAN THREE-MANIFOLDS

Cites Work

• Lorentz manifolds modelled on a Lorentz symmetric space
• Curvature homogeneous spaces with a solvable Lie group as homogeneous model
• On curvature homogeneity of Riemannian manifolds
• Non-homogeneous relatives of symmetric spaces
• A characterization of locally homogeneous Riemann manifolds of dimension 3
• Isometry groups of three-dimensional Riemannian metrics
• On the Riemannian manifolds of the form $B\times_{f}F$
• A classification of Riemannian 3-manifolds with constant principal ricci curvaturesρ₁= ρ₂≠ ρ₃
• On spacetimes admitting shear-free, irrotational, geodesic time-like congruences
• Shear-free, irrotational, geodesic, anisotropic fluid cosmologies
• Lorentzian three-metrics with degenerate Ricci tensors
• Infinitesimally homogeneous spaces

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