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Gradient Ricci Solitons with Structure of Warped Product

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Abstract

In this paper we consider semi-Riemannian warped product gradient Ricci solitons. We prove that the potential function depends only on the base and the fiber is necessarily Einstein manifold. We provide all such solutions in the case of steady gradient Ricci solitons when the base is conformal to an n-dimensional pseudo-Euclidean space, invariant under the action of an (n − 1)-dimensional translation group, and the fiber is Ricci-flat.

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Authors and Affiliations

  1. ICET-CUA, Universidade Federal de Mato Grosso, Av. Universitária no. 3.500, Pontal do Araguaia, MT, Brazil

    Márcio Lemes de Sousa

  2. IME, Universidade Federal de Goiás, Caixa Postal 131, Goiânia, GO, 74001-970, Brazil

    Romildo Pina

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  1. Márcio Lemes de Sousa
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  2. Romildo Pina
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Correspondence to Romildo Pina.

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R. Pina was partially supported by CAPES-PROCAD.

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Lemes de Sousa, M., Pina, R. Gradient Ricci Solitons with Structure of Warped Product. Results Math 71, 825–840 (2017). https://doi.org/10.1007/s00025-016-0583-2

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  • DOI: https://doi.org/10.1007/s00025-016-0583-2

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