Abstract
Geometry of four dimensional pseudo-Riemannian Lie groups of signature (2, 2) studied. A rich family of Einstein, locally symmetric and conformally flat examples is presented.
Similar content being viewed by others
References
Arias-Marco, T., Kowalski, O.: Classification of 4-dimensional homogeneous D’Atri spaces. Czechoslov. Math. J. 58(133), 203–239 (2008)
Bérard-Bérgery, L.: Homogeneous Riemannian Spaces of Dimension Four. Seminar A. Besse, Four Dimensional Riemannian Geometry. Mir, Moscow (Russian) (1985)
Calvaruso, G.: Homogeneous structures on three-dimensional Lorentzian manifolds. J. Geom. Phys. 57(4), 1279–1291 (2007)
Calvaruso, G., Zaeim, A.: Four-dimensional Lorentzian Lie groups. Differ. Geom. Appl. 31(4), 496–509 (2013)
Calvaruso, G., Zaeim, A.: Neutral metrics on four-dimensional Lie groups. Lie Theory J. 25, 1023–1044 (2015)
Cordero, L.A., Parker, P.E.: Left-invariant Lorentzian metrics on 3-dimensional Lie groups. Rend. Mat. Appl. 17(1), 129–155 (1997)
Haji-Badali, A., Karami, R.: Ricci solitons on four-dimensional neutral Lie groups. J. Lie Theory 27(4), 943–967 (2017)
Haji-Badali, A., Zaeim, A.: Commutative curvature operators over four-dimensional homogeneous manifolds. Int. J. Geom. Methods Mod. Phys. 12(10), 1550123 (2015)
Komrakov Jnr, B.: Einstein–Maxwell equation on four-dimensional homogeneous spaces. Lobachevskii J. Math. 8, 33–165 (2001)
O’Neill, B.: Semi-Riemannian Geometry. Academic Press, New York (1983)
Rahmani, S.: Métriques de Lorentz sur les groupes de Lie unimodulaires de dimension trois. J. Goem. Phys. 9, 295–302 (1992)
Tricerri, F., Vanhecke, L.: Homogeneous Structures on Riemannian Manifolds. London Mathematical Society Lecture Notes, vol. 83. Cambridge University Press, Cambridge (1983)
Zaeim, A.: Einstein-like Lorentzian Lie groups of dimension four. J. Nonlinear Math. Phys. 24(4), 556–570 (2017)
Zaeim, A., Haji-Badali, A.: Einstein-like pseudo-Riemannian homogeneous manifolds of dimension four. Mediter. J. Math. 13(5), 3455–3468 (2016)
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Zaeim, A., Karami, R. Geometric Consequences of Four Dimensional Neutral Lie Groups. Bull Braz Math Soc, New Series 50, 167–186 (2019). https://doi.org/10.1007/s00574-018-0097-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00574-018-0097-5