Abstract
In this paper we consider \(\rho \)-Einstein solitons that are conformal to a pseudo-Euclidean space and invariant under the action of the pseudo-orthogonal group. We provide all the solutions for the gradient Schouten soliton case. Moreover, we proved that if a gradient Schouten soliton is both complete, conformal to a Euclidean metric, and rotationally symmetric, then it is isometric to \({\mathbb {R}}\times {\mathbb {S}}^{n-1}\).
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The authors would like to thank the referee for his careful reading, relevant remarks, and valuable suggestion.
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Pina, R., Menezes, I. On gradient Schouten solitons conformal to a pseudo-Euclidean space. manuscripta math. 163, 395–406 (2020). https://doi.org/10.1007/s00229-019-01159-0
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DOI: https://doi.org/10.1007/s00229-019-01159-0