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<p>In this paper, the authors study gradient Ricci-Harmonic solitons on warped product manifolds. First, they prove triviality results for the potential and warping functions that reach a maximum or a minimum. In order to provide nontrivial examples, they consider the base and the fiber conformal to a semi-Euclidean space, which is invariant under the action of a translation group of co-dimension one. This approach allows them to produce infinitely many examples of geodesically complete semi-Riemannian Ricci-Harmonic solitons not present in the literature.</p>

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On Warped Product Gradient Ricci-Harmonic Soliton

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Elismar Batista,
  • Levi Adriano,
  • Willian Tokura

摘要

In this paper, the authors study gradient Ricci-Harmonic solitons on warped product manifolds. First, they prove triviality results for the potential and warping functions that reach a maximum or a minimum. In order to provide nontrivial examples, they consider the base and the fiber conformal to a semi-Euclidean space, which is invariant under the action of a translation group of co-dimension one. This approach allows them to produce infinitely many examples of geodesically complete semi-Riemannian Ricci-Harmonic solitons not present in the literature.