On Warped Product Gradient Ricci-Harmonic Soliton

Abstract

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.

Keywords

Warped product / Gradient Ricci-Harmonic solitons / Semi-Riemannian metric / Group action / 58J60 / 53C25 / 53C21

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