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Journal of Geometric Analysis

, Volume 23, Issue 3, pp 1196–1212 | Cite as

Locally Conformally Flat Lorentzian Gradient Ricci Solitons

  • M. Brozos-VázquezEmail author
  • E. García-Río
  • S. Gavino-Fernández
Article

Abstract

It is shown that locally conformally flat Lorentzian gradient Ricci solitons are locally isometric to a Robertson–Walker warped product, if the gradient of the potential function is nonnull, and to a plane wave, if the gradient of the potential function is null. The latter gradient Ricci solitons are necessarily steady.

Keywords

Ricci solitons Gradient Ricci solitons Lorentzian locally conformally flat manifolds 

Mathematics Subject Classification (2000)

53C21 53C50 53C25 

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Copyright information

© Mathematica Josephina, Inc. 2011

Authors and Affiliations

  • M. Brozos-Vázquez
    • 1
    Email author
  • E. García-Río
    • 2
  • S. Gavino-Fernández
    • 2
  1. 1.Department of MathematicsUniversity of A CoruñaA CoruñaSpain
  2. 2.Faculty of MathematicsUniversity of Santiago de CompostelaSantiago de CompostelaSpain

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