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Locally Conformally Flat Lorentzian Gradient Ricci Solitons

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of A Coruña, A Coruña, Spain

    M. Brozos-Vázquez

  2. Faculty of Mathematics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    E. García-Río & S. Gavino-Fernández

Authors
  1. M. Brozos-Vázquez
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  2. E. García-Río
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  3. S. Gavino-Fernández
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Corresponding author

Correspondence to M. Brozos-Vázquez.

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Communicated by Peter B. Gilkey.

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Brozos-Vázquez, M., García-Río, E. & Gavino-Fernández, S. Locally Conformally Flat Lorentzian Gradient Ricci Solitons. J Geom Anal 23, 1196–1212 (2013). https://doi.org/10.1007/s12220-011-9283-z

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  • DOI: https://doi.org/10.1007/s12220-011-9283-z

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