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A note on locally conformally flat gradient Ricci solitons

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Abstract

We show that locally conformally flat gradient Ricci solitons, possibly incomplete, are locally isometric to a warped product of an interval and a space form. Consequently, we get that complete gradient shrinking and steady Ricci solitons with vanishing Weyl tensor are rotationally symmetric, from which their classification follows.

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Acknowledgments

The Authors would like to thank the Referee for a careful reading and all the suggestions which resulted in an improved version of our original manuscript.

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Authors and Affiliations

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

    Manuel Fernández-López  & Eduardo García-Río

Authors
  1. Manuel Fernández-López
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  2. Eduardo García-Río
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Correspondence to Eduardo García-Río.

Additional information

Supported by projects MTM2009-07756 and INCITE09 207 151 PR (Spain).

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Fernández-López , M., García-Río, E. A note on locally conformally flat gradient Ricci solitons. Geom Dedicata 168, 1–7 (2014). https://doi.org/10.1007/s10711-012-9815-0

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  • DOI: https://doi.org/10.1007/s10711-012-9815-0

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