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Invariant solutions for gradient Ricci almost solitons

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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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Correspondence to Benedito Leandro.

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Romildo Pina: Partially supported by CAPES-PROCAD.

Communicated by Claudio Gorodski.

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Leandro, B., Pina, R. & Bezerra, T.P.F. Invariant solutions for gradient Ricci almost solitons. São Paulo J. Math. Sci. (2020) doi:10.1007/s40863-019-00161-4

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Keywords

  • Semi-Riemannian metric
  • Gradient Ricci solitons
  • Warped product

Mathematics Subject Classification

  • 53C21
  • 53C50
  • 53C25