Lobachevskii Journal of Mathematics

, Volume 39, Issue 2, pp 191–194 | Cite as

Ricci Solitons on Lorentzian Walker Manifolds of Low Dimension



The Ricci soliton equation on four-dimensional conformally flat Lorentzian Walker manifolds is investigated, non-trivial solutions are found. New Ricci soliton metrics on three dimensional Lorentzian Walker manifolds are obtained.

Keywords and phrases

Ricci soliton Walker manifold conformally flat metric 


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  1. 1.
    R. S. Hamilton, “The Ricci flow on surfaces,” Contemp. Math. 71, 237–262 (1988).MathSciNetCrossRefGoogle Scholar
  2. 2.
    H.-D. Cao, “Recent progress on Ricci solitons,” Adv. Lect.Math. 11, 1–38 (2010).MathSciNetMATHGoogle Scholar
  3. 3.
    M. Brozos-Vazquez, E. Garcia-Rio, and S. Gavino-Fernandez, “Locally conformally flat Lorentzian gradient Ricci solitons,” J. Geom. Anal. 23, 1196–1212 (2013).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    M. Brozos-Vazquez, E. Garcia-Rio, P. Gilkey, S. Nikcevic, and R. Vazquez-Lorenzo, The Geometry of Walker Manifolds, Vol. 5 of Synthesis Lectures on Mathematics and Statistics (Morgan and Claypool, San Rafael, CA, 2009).MATHGoogle Scholar
  5. 5.
    A. S. Galaev, “Conformally flat Lorentzian manifolds with special holonomy groups,” Sb.: Math. 204 (9), 29–50 (2013).MathSciNetMATHGoogle Scholar
  6. 6.
    M. Brozos-Vazquez, G. Calvaruso, E. Garcia-Rio, and S. Gavino-Fernandez, “Three-dimensional Lorentzian homogeneous Ricci solitons,” Israel J. Math. 188, 385–403 (2012).MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    W. Batat, M. Brozos-Vazquez, E. Garcia-Rio, and S. Gavino-Fernandez, “Ricci solitons on Lorentzian manifolds with large isometry groups,” Bull. London Math. Soc. 43, 1219–1227 (2011).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • I. V. Ernst
    • 1
  • D. N. Oskorbin
    • 1
  • E. D. Rodionov
    • 1
  1. 1.Altai State UniversityBarnaulRussia

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