Invariant solutions for gradient Ricci almost solitons

  • Benedito LeandroEmail author
  • Romildo Pina
  • Tatiana Pires Fleury Bezerra
Original Paper


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.


Semi-Riemannian metric Gradient Ricci solitons Warped product 

Mathematics Subject Classification

53C21 53C50 53C25 



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Copyright information

© Instituto de Matemática e Estatística da Universidade de São Paulo 2020

Authors and Affiliations

  • Benedito Leandro
    • 1
    Email author
  • Romildo Pina
    • 1
  • Tatiana Pires Fleury Bezerra
    • 2
  1. 1.IMEUniversidade Federal de GoiásGoiâniaBrazil
  2. 2.IFG -Instituto Federal de Educação, Ciência e Tecnologia de GoiásAp. de GoiâniaBrazil

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