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Geometry of gradient Yamabe solitons

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Abstract

We prove that the gradient of the potential function is bounded for gradient Yamabe solitons if the scalar curvature satisfies some boundedness conditions. Suppose in addition the Weyl tensor is harmonic, we prove that the Riemannian curvature and its derivatives are bounded in the 4-dimensional case.

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Authors and Affiliations

  1. School of Mathematics and Physics, China University of Geosciences, Wuhan, People’s Republic of China

    Fei Yang & Liangdi Zhang

Authors
  1. Fei Yang
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  2. Liangdi Zhang
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Correspondence to Liangdi Zhang.

Additional information

This paper is supported by Tian Yuan Special Funds of the National Natural Science Foundation of China (No. 11326076).

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Yang, F., Zhang, L. Geometry of gradient Yamabe solitons. Ann Glob Anal Geom 50, 367–379 (2016). https://doi.org/10.1007/s10455-016-9516-2

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  • DOI: https://doi.org/10.1007/s10455-016-9516-2

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