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Abstract In this paper, we consider the self-similar solutions to the hyperbolic geometric flow, called hyperbolic Ricci solitons. Also, we investigate hyperbolic Ricci solitons on three-dimensional homogeneous manifolds with Riemannian and Lorentzian metrics and obtain some hyperbolic Ricci solitons on such manifolds.
Faraji et al. (Sat,) studied this question.