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Geometric Consequences of Four Dimensional Neutral Lie Groups

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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.

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References

  • Arias-Marco, T., Kowalski, O.: Classification of 4-dimensional homogeneous D’Atri spaces. Czechoslov. Math. J. 58(133), 203–239 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • Calvaruso, G., Zaeim, A.: Four-dimensional Lorentzian Lie groups. Differ. Geom. Appl. 31(4), 496–509 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • Calvaruso, G., Zaeim, A.: Neutral metrics on four-dimensional Lie groups. Lie Theory J. 25, 1023–1044 (2015)

    MathSciNet  MATH  Google Scholar 

  • Cordero, L.A., Parker, P.E.: Left-invariant Lorentzian metrics on 3-dimensional Lie groups. Rend. Mat. Appl. 17(1), 129–155 (1997)

    MathSciNet  MATH  Google Scholar 

  • Haji-Badali, A., Karami, R.: Ricci solitons on four-dimensional neutral Lie groups. J. Lie Theory 27(4), 943–967 (2017)

    MathSciNet  MATH  Google Scholar 

  • Haji-Badali, A., Zaeim, A.: Commutative curvature operators over four-dimensional homogeneous manifolds. Int. J. Geom. Methods Mod. Phys. 12(10), 1550123 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • Komrakov Jnr, B.: Einstein–Maxwell equation on four-dimensional homogeneous spaces. Lobachevskii J. Math. 8, 33–165 (2001)

    MathSciNet  MATH  Google Scholar 

  • O’Neill, B.: Semi-Riemannian Geometry. Academic Press, New York (1983)

    MATH  Google Scholar 

  • Rahmani, S.: Métriques de Lorentz sur les groupes de Lie unimodulaires de dimension trois. J. Goem. Phys. 9, 295–302 (1992)

    Article  MATH  Google Scholar 

  • Tricerri, F., Vanhecke, L.: Homogeneous Structures on Riemannian Manifolds. London Mathematical Society Lecture Notes, vol. 83. Cambridge University Press, Cambridge (1983)

    Book  MATH  Google Scholar 

  • Zaeim, A.: Einstein-like Lorentzian Lie groups of dimension four. J. Nonlinear Math. Phys. 24(4), 556–570 (2017)

    Article  MathSciNet  Google Scholar 

  • Zaeim, A., Haji-Badali, A.: Einstein-like pseudo-Riemannian homogeneous manifolds of dimension four. Mediter. J. Math. 13(5), 3455–3468 (2016)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

    Amirhesam Zaeim

  2. Department of Mathematics, Basic Sciences Faculty, University of Bonab, Bonab, 55517, Iran

    Ramisa Karami

Authors
  1. Amirhesam Zaeim
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  2. Ramisa Karami
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Correspondence to Amirhesam Zaeim.

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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

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  • DOI: https://doi.org/10.1007/s00574-018-0097-5

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