Advertisement

Lobachevskii Journal of Mathematics

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

Ricci Solitons on Lorentzian Walker Manifolds of Low Dimension

  • I. V. Ernst
  • D. N. Oskorbin
  • E. D. Rodionov
Article
  • 17 Downloads

Abstract

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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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).MathSciNetzbMATHGoogle 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).MathSciNetCrossRefzbMATHGoogle 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).zbMATHGoogle Scholar
  5. 5.
    A. S. Galaev, “Conformally flat Lorentzian manifolds with special holonomy groups,” Sb.: Math. 204 (9), 29–50 (2013).MathSciNetzbMATHGoogle 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).MathSciNetCrossRefzbMATHGoogle 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).MathSciNetCrossRefzbMATHGoogle 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

Personalised recommendations