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Immersions of r-almost Yamabe solitons into Riemannian Manifolds

Abstract

We establish the concept of r-almost Yamabe soliton immersed into a Riemannian manifold, which extends in a natural way the notion of almost Yamabe solitons introduced by Barbosa and Ribeiro in [3]. In this setting, under suitable hypothesis on the potential and soliton functions, we prove nonexistence and characterization results. Moreover, some examples of these new geometric objects are presented.

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Acknowledgements

The authors would like to thank the referee for his/her valuable suggestions and useful comments which improved the paper. We would also like to thank Cícero Aquino for comments and valuable conversations. The first author is partially supported by CNPq, Brazil (Grant: 430998/2018-0) and FAPEPI (PPP-Edital 007/ 2018).

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Correspondence to Eudes L. de Lima.

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Cunha, A.W., de Lima, E.L. Immersions of r-almost Yamabe solitons into Riemannian Manifolds. manuscripta math. (2021). https://doi.org/10.1007/s00229-021-01343-1

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Mathematics Subject Classification

  • Primary 53C20
  • 53C21
  • 53C25
  • 53C42