The Lorentzian oscillator group as a geodesic orbit space

9 pags. ; 2 tab. ; PACS numbers: 02.20.Qs, 04.65,+eWe 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 twenty-four of the thirty-two possible supersymmetries.The three authors have been partially supported by the Ministry of Economy and Competitiveness, Spain, under Project MTM2011-22528.Peer reviewe

Homogeneous quaternionic Kähler structures on rank-three Alekseevsky spaces

15 págs. ; 2 tabs. ; A.M.S. Subject Classi cation 2010: 53C26, 53C30.The homogeneous quaternionic K ahler structures on the rank-three Alekseevsky spaces with their natural quaternionic structures, when each of them is described as a solvable Lie group, and their types in Fino's classi cation, are found.The 1rst author has been partially supported by the ENSET d'Oran, Algeria. The second and third authors have been partially supported by the Ministry of Science and Innovation, Spain, under Project MTM2008{01386.Peer reviewe

Homogeneous Riemannian structures on some solvable extensions of the Heisenberg group

17 pags.Two families of four or five-dimensional Riemannian solvable Lie groups, which are extensions of the 3-dimensional Heisenberg group, are considered.We determine all the homogeneous Riemannian structures on them, and the simply connected groups of isometries corresponding to the associated reductive decompositions. Some of these structures are homogeneousK¨ahler or homogeneous cosymplectic, and in these cases they are realized by the complex hyperbolic plane CH(2) and by CH(2)×R, respectively.Ministry of Science and Innovation, Spain, under Project MTM2011-22528

Homogeneous pseudo-Riemannian structures of linear type

Homogeneous pseudo-Riemannian structures of linear type are reviewed and studied. In the Riemannian case, they furnish characterisations of the real, complex and quaternionic hyperbolic spaces. In the Lorentzian case, a related class gives characterisations of singular homogeneous plane waves.MICINN-CSIC MTM2008-01863 ENSET, ORAN, ALGERIAPeer reviewe

Hamiltonian systems on k-cosymplectic manifolds

The Hamiltonian framework on symplectic and cosymplectic manifolds is extended in order to consider classical field theories. To do this, the notion of k-cosymplectic manifold is introduced, and a suitable Hamiltonian formalism is developed so that the field equations for scalar and vector Hamiltonian functions are derived. © 1998 American Institute of Physics.This work has been partially supported through grants DGICYT (Spain) (Project No. PB94- 0106) and XUNTA DE GALICIA (Projects No. XUGA13101A94 and No. XUGA13101A96). MdL also acknowledges the support by FAPERJ-Proc. E-26/170.236/96. info:eu-repo/grantAgreement/EC/FP7/Peer Reviewe

The oscillator group as a homogeneous spacetime

Some results on the oscillator group are reported. Specifically: some of their properties as a causal homogeneous spacetime; the oscillator group as a symmetric Lorentzian space which is solution of sourceless Einstein-Yang-Mills equations; the Lorentzian homogeneous structures and their associated groups of isometries on the oscillator group with left-invariant Lorentzian metrics; the Lorentzian homogeneous structures associated to a bi-invariant metric; and then the oscillator group as solution of Einstein-Yang-Mills equations with sources.Partially supported by DGES (Spain) under Project PB95-0124 and by Xuna de Galicia under Project SUGA 20703B98Peer Reviewe