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Some Results on Conformal Geometry of Gradient Ricci Solitons

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Abstract

The goal of this article is to study the conformal geometry of gradient Ricci solitons as well as the relationship between such Riemannian manifolds and closed conformal vector fields. We prove that gradient Ricci solitons endowed with a non-parallel closed conformal vector field can be conformally changed to constant scalar curvature almost everywhere. Moreover, we obtain a characterization for this class of manifolds under assumption that the closed conformal vector field is gradient type.

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Acknowledgements

The author want to thank the referee for the relevant remarks and valuable suggestions.

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  1. Instituto de Ciências Exatas e da Natureza, Universidade da Integração Internacional da Lusofonia Afro-Brasileira, Campus das Auroras, Rua José Franco de Oliveira, 62790-970, Redenção, CE, Brazil

    J. F. Silva Filho

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  1. J. F. Silva Filho
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Correspondence to J. F. Silva Filho.

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Filho, J.F.S. Some Results on Conformal Geometry of Gradient Ricci Solitons. Bull Braz Math Soc, New Series 51, 937–955 (2020). https://doi.org/10.1007/s00574-019-00182-9

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  • DOI: https://doi.org/10.1007/s00574-019-00182-9

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