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On non-compact Cotton solitons

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Abstract

This work aims to provide some triviality results for complete Cotton solitons under different assumptions like non-positive Ricci curvature, convergence to zero at infinity, polynomial or volume growth, and stochastic completeness. Finally, as an application, we classify the Cotton solitons with additional curative condition to be isometric to a space form of constant sectional curvature or to a Riemannian product \(M^2(c)\times N^1\), where \(N^1={\mathbb {R}}^1\) or \({\mathbb {S}}^1\) for some c.

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Acknowledgements

The authors would like to thank Erin Griffin for her valuable suggestions and comments. Also, the authors would like to thank the referee for his/her comments about the writing which were very helpful in improving this work. The first author is partially supported by CNPq, Brazil (Grant: 430998/2018-0) and FAPEPI (PPP-Edital 007/ 2018). The second author is partially by CAPES-Brazil.

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  1. Departamento de Pós-Graduação em Matemática, Universidade Federal do Piauí, Teresina, Piauí, 64049-550, Brazil

    Antonio W. Cunha & Antonio N. Silva Junior

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  1. Antonio W. Cunha
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  2. Antonio N. Silva Junior
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Correspondence to Antonio W. Cunha.

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Cunha, A.W., Silva Junior, A.N. On non-compact Cotton solitons. Lett Math Phys 112, 87 (2022). https://doi.org/10.1007/s11005-022-01582-7

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  • DOI: https://doi.org/10.1007/s11005-022-01582-7

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