The Lorentzian oscillator group as a geodesic orbit space

W. Batat, P. M. Gadea, J. A. Oubiña
2012 Journal of Mathematical Physics  
We prove that the four-dimensional oscillator group Os endowed with any of its usual left-invariant Lorentzian metrics, is a Lorentzian geodesic (so in particular null-geodesic) orbit space with some of its homogeneous descriptions, corresponding to certain homogeneous Lorentzian structures. Each time that Os is endowed with a suitable metric and an appropriate homogeneous Lorentzian structure, it is a candidate for constructing solutions in eleven-dimensional supergravity with at least
more » ... th at least twenty-four of the thirty-two possible supersymmetries.
doi:10.1063/1.4754702 fatcat:2dgo2lw4wvajpay64gd4xnebgi