Reductive decompositions and Einstein–Yang–Mills equations associated to the oscillator group

DOI10.1063/1.532902zbMath0978.53095OpenAlexW2071852453MaRDI QIDQ4270361

Raúl Durán Díaz, Pedro Martínez Gadea, Jose A. Oubina

Publication date: 21 November 1999

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

Full work available at URL: https://doi.org/10.1063/1.532902

zbMATH Keywords

Einstein-Yang-Mills equationsoscillator groupbi-invariant Lorentzian metrichomogeneous Lorentzian structures

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Nilpotent and solvable Lie groups (22E25) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (12)

Kundt three-dimensional left invariant spacetimes ⋮ Oscillator spacetimes are Ricci solitons ⋮ On the symmetries of the Lorentzian oscillator group ⋮ A class of nilpotent Lie algebras admitting a compact subgroup of automorphisms ⋮ Totally geodesic and parallel hypersurfaces of four-dimensional oscillator groups ⋮ Conformal Geometry of Semi-Direct Extensions of the Heisenberg Group ⋮ Harmonicity of vector fields on the oscillator groups with neutral signature ⋮ Lorentzian symmetric spaces which are Einstein-Yang-Mills with respect to invariant metric connections ⋮ Poisson algebras and symmetric Leibniz bialgebra structures on oscillator Lie algebras ⋮ Invariant harmonic unit vector fields on the oscillator groups ⋮ The Lorentzian oscillator group as a geodesic orbit space ⋮ Some remarks on the oscillator group

Cites Work

• Methods of investigation of the causal structures of homogeneous Lorentz manifolds
• 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
• The oscillator parallelization of the induced scalar bundle
• On homogeneous Riemannian manifolds
• The representations of the oscillator group
• Decomposition of a vector field in a parallelized induced bundle

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