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

Abstract

Almost Ricci-like solitons on almost contact B-metric manifolds with torse-forming potential have been studied. The case in which this potential is further vertical is considered, i.e. the potential is pointwise collinear to the Reeb vector field. The conditions under which the investigated manifolds with almost Ricci-like solitons are equivalent to almost Einstein-like manifolds have been established. In this case, necessary and sufficient conditions have been found for a number of properties of the curvature tensor and its Ricci tensor. Then some results are obtained for a parallel symmetric second-order covariant tensor on the manifolds under study. Finally, an explicit example of an arbitrary dimension is given and some of the results are illustrated.