The Lorentzian oscillator group as a geodesic orbit space

DOI10.1063/1.4754702zbMath1282.83057OpenAlexW2030851793MaRDI QIDQ2872300

Wafaa Batat, Jose A. Oubina, Pedro Martínez Gadea

Publication date: 14 January 2014

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

Full work available at URL: https://semanticscholar.org/paper/b8a8316fb2690dd3e5ebbc112751c2d9fa52bcb8

zbMATH Keywords

supergravitysolvable Lie groupalgebra Osbi-invariant Lorentzian metricLorentzian geodesic

Mathematics Subject Classification ID

Supergravity (83E50) Applications of Lie groups to the sciences; explicit representations (22E70) Applications of differential geometry to physics (53Z05) Geodesics in global differential geometry (53C22) Exact solutions to problems in general relativity and gravitational theory (83C15) Lie algebras of linear algebraic groups (17B45) Equations of motion in general relativity and gravitational theory (83C10) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (2)

Four-dimensional pseudo-Riemannian g.o. spaces and manifolds ⋮ Homogeneous Lorentzian structures of 4-dimensional nilpotent Lie groups

Cites Work

• Unnamed Item
• Solutions of the Yang-Baxter equations on quadratic Lie groups: the case of oscillator groups
• Les groupes oscillateurs et leurs réseaux. (Oscillator groups and their lattices)
• Groupes de Lie munis de métriques bi-invariantes. (Lie groups admitting bi-invariant metrics)
• Chronogeometry of an electromagnetic wave given by a bi-invariant metric on the oscillator group
• Reductive homogeneous pseudo-Riemannian manifolds
• Geometry of oscillator groups and locally symmetric manifolds
• New examples of Riemannian g.o. manifolds in dimension 7
• Homogeneous geodesics in solvable Lie groups
• Homogeneous Lorentzian structures on the oscillator groups
• On homogeneous Riemannian manifolds
• Homogeneous Lorentzian spaces whose null-geodesics are canonically homogeneous
• Homogeneous Lorentzian spaces admitting a homogeneous structure of type \(\mathcal T_{1} \oplus \mathcal T_{3}\)
• Penrose limits of homogeneous spaces
• The representations of the oscillator group
• A homogeneous space–time model with singularities
• Survey on homogeneous geodesics
• Reductive decompositions and Einstein–Yang–Mills equations associated to the oscillator group
• Wess-Zumino-Witten model based on a nonsemisimple group
• Supersymmetry and homogeneity of M-theory backgrounds
• Invariant Affine Connections on Homogeneous Spaces

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