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A generalization of Ricci-like solitons with torse-forming potential, whichis a constant multiple of the Reeb vector field, is studied. The conditionsunder which these solitons are equivalent to almost Einstein-like metrics aregiven. Some results are obtained for a parallel symmetric second-ordercovariant tensor. Finally, an explicit example of an arbitrary dimension isgiven and some of the results are illustrated.

Almost Ricci-like solitons with torse-forming vertical potential of constant length on almost contact B-metric manifolds