Abstract
In this paper we provide an ansatz that reduces a pseudo-Riemannian gradient Ricci almost soliton (PDE) into an integrable system of ODE. First, considering a warped structure with conformally flat base invariant under the action of an \((n-1)\)-dimensional translation group and semi-Riemannian Einstein fiber, we provide the ODE system which characterizes all such solitons. Then, we also provide a classification for a conformally flat pseudo-Riemannian gradient Ricci almost soliton invariant by the actions of a translation group or a pseudo-orthogonal group. Finally, we conclude with some explicit examples.
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Communicated by Claudio Gorodski.
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Romildo Pina: Partially supported by CAPES-PROCAD.
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Leandro, B., Pina, R. & Bezerra, T.P.F. Invariant solutions for gradient Ricci almost solitons. São Paulo J. Math. Sci. 14, 123–138 (2020). https://doi.org/10.1007/s40863-019-00161-4
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DOI: https://doi.org/10.1007/s40863-019-00161-4