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Gradient Ricci solitons with a conformal vector field

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Abstract

We show that a connected gradient Ricci soliton (\(M,g,f,\lambda \)) with constant scalar curvature and admitting a non-homothetic conformal vector field V leaving the potential vector field invariant, is Einstein and the potential function f is constant. For locally conformally flat case and non-homothetic V we show without constant scalar curvature assumption, that f is constant and g has constant curvature.

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Correspondence to Ramesh Sharma.

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Sharma, R. Gradient Ricci solitons with a conformal vector field. J. Geom. 109, 33 (2018). https://doi.org/10.1007/s00022-018-0439-x

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  • DOI: https://doi.org/10.1007/s00022-018-0439-x

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