Ricci-like solitons on almost contact B-metric manifolds

Abstract

Ricci-like solitons with potential Reeb vector field are introduced and studied on almost contact B-metric manifolds. The cases of Sasaki-like manifolds and torse-forming potentials have been considered. In these cases, it is proved that the manifold admits a Ricci-like soliton if and only if the structure is Einstein-like. Explicit examples of Lie groups as 3- and 5-dimensional manifolds with the structures studied are provided.