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Ricci almost solitons on semi‐Riemannian warped products

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  • Valter Borges
  • Keti Tenenblat

Abstract

It is shown that a gradient Ricci almost soliton on a warped product, (Bn×hFm,g,f,λ)$\big (B^n\times _h F^m, g,f,\lambda \big )$ whose potential function f depends on the fiber, is either a Ricci soliton or λ is not constant and the warped product, the base and the fiber are Einstein manifolds, which admit conformal vector fields. Assuming completeness, a classification is provided for the gradient Ricci almost solitons on warped products, whose potential functions depend on the fiber. An important decomposition property of the potential function in terms of functions which depend either on the base or on the fiber is proven. In the case of a complete gradient Ricci soliton, the potential function depends only on the base.

Suggested Citation

  • Valter Borges & Keti Tenenblat, 2022. "Ricci almost solitons on semi‐Riemannian warped products," Mathematische Nachrichten, Wiley Blackwell, vol. 295(1), pages 22-43, January.
    • Handle: RePEc:bla:mathna:v:295:y:2022:i:1:p:22-43
    DOI: 10.1002/mana.201900242
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    References listed on IDEAS

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    1. Sezgin Altay Demirbağ & Sinem Güler, 2017. "Rigidity of ( m , ρ ) -quasi Einstein manifolds," Mathematische Nachrichten, Wiley Blackwell, vol. 290(14-15), pages 2100-2110, October.
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