Curvature operators and generalizations of symmetric spaces in Lorentzian geometry

DOI10.1515/advgeom.2011.036zbMath1260.53122OpenAlexW2319875263MaRDI QIDQ2891069

Eduardo García-Río, Ramón Vázquez-Lorenzo, M. Elena Vázquez-Abal, Esteban Calviño-Louzao

Publication date: 13 June 2012

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

Full work available at URL: https://doi.org/10.1515/advgeom.2011.036

zbMATH Keywords

homogeneous spacesLie groupsskew-symmetric curvature operatorcurvature homogeneityJacobi operato

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Differential geometry of symmetric spaces (53C35) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (2)

Three-dimensional homogeneous Lorentzian Yamabe solitons ⋮ Homogeneity of Lorentzian three-manifolds with recurrent curvature

Cites Work

• Einstein-like curvature homogeneous Lorentzian three-manifolds
• Two natural generalizations of locally symmetric spaces
• Lorentz metrics on unimodular Lie groups of dimension three
• Einstein-like manifolds which are not Einstein
• Riemannian manifolds in which certain curvature operator has constant eigenvalues along each circle
• The Ledger curvature conditions and D'Atri geometry
• Three-dimensional Lorentz metrics and curvature homogeneity of order one
• Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds
• LORENTZIAN 3-MANIFOLDS WITH COMMUTING CURVATURE OPERATORS
• Einstein-Like Lorentz Metrics and Three-Dimensional Curvature Homogeneity of Order One
• Lorentzian three-manifolds with special curvature operators

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