Flat pseudo-Riemannian Lie groups

DOI10.2748/tmj/1113247126zbMath1058.53055OpenAlexW2047864437MaRDI QIDQ1876281

Alberto Medina, Anne-Marie Aubert

Publication date: 16 August 2004

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1113247126

zbMATH Keywords

affine Lie groupshomogeneous geometric stuctures

Mathematics Subject Classification ID

Lie algebras of Lie groups (22E60) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (20)

Flat affine or projective geometries on Lie groups ⋮ Left invariant special Kähler structures ⋮ Flat affine symplectic Lie groups ⋮ Classification of Einstein Lorentzian 3-nilpotent Lie groups with 1-dimensional nondegenerate center ⋮ Flat affine manifolds and their transformations ⋮ Flat symplectic Lie algebras ⋮ Left invariant Ricci flat metrics on Lie groups ⋮ A left-symmetric algebraic approach to left invariant flat (pseudo-)metrics on Lie groups ⋮ On pseudo-Euclidean Novikov algebras ⋮ On a remarkable class of flat pseudo-Riemannian Lie groups ⋮ Solutions of the Yang-Baxter equations on quadratic Lie groups: the case of oscillator groups ⋮ On a class of Lie groups with a left invariant flat pseudo-metric ⋮ On Einstein Lorentzian nilpotent Lie groups ⋮ Existence of left invariant Ricci flat metrics on nilpotent Lie groups ⋮ Diagram involutions and homogeneous Ricci-flat metrics ⋮ Flat left-invariant pseudo-Riemannian metrics on unimodular Lie groups ⋮ Flat Nonunimodular Lorentzian Lie Algebras ⋮ Flat compact Hermite-Lorentz manifolds in dimension 4 ⋮ Flat left-invariant pseudo-Riemannian metrics on quadratic Lie groups ⋮ On flat pseudo-Euclidean nilpotent Lie algebras

Cites Work

• Homogeneous Hessian manifolds
• Flat left-invariant connections adapted to the automorphism structure of a Lie group
• On certain locally flat homogeneous manifolds of solvable Lie groups
• Curvatures of left invariant metrics on Lie groups
• On fundamental groups of complete affinely flat manifolds
• Radical d'une algèbre symétrique à gauche
• Symplectic double extension of a symplectic Lie group
• On a class of common properties of some different types of algebras.
• Algèbres de Lie et produit scalaire invariant
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