Three-dimensional complete gradient Yamabe solitons with divergence-free Cotton tensor


In this paper, we classify three-dimensional complete gradient Yamabe solitons with divergence-free Cotton tensor. We also give some classifications of complete gradient Yamabe solitons with nonpositively curved Ricci curvature in the direction of the gradient of the potential function.

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  • 07 July 2020

    In the original article the formula chapter 4, just above Remark 4.2 in the paragraph starting with Case (2) the formula should read.


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The work was done while the author was visiting the Department of Mathematics of Texas A & M University-Commerce as a Visiting Scholar, and he is grateful to the department and the university for the hospitality he had received during the visit. He also would like to thank the referee for his/her valuable comments and suggestions.

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Correspondence to Shun Maeta.

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The author is partially supported by the Grant-in-Aid for Young Scientists, Nos. 15K17542 and 19K14534 Japan Society for the Promotion of Science, and JSPS Overseas Research Fellowships 2017-2019 No. 70.

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Maeta, S. Three-dimensional complete gradient Yamabe solitons with divergence-free Cotton tensor. Ann Glob Anal Geom (2020).

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  • Yamabe solitons
  • Cotton tensor
  • Bach tensor
  • Scalar curvature

Mathematics Subject Classification

  • 53C21
  • 53C25
  • 53C20