Pairs of associated Yamabe almost solitons with vertical potential on almost contact complex Riemannian manifolds

Abstract

Almost contact complex Riemannian manifolds, known also as almost contact B-metric manifolds, are in principle equipped with a pair of mutually associated pseudo-Riemannian metrics. Each of these metrics is specialized here as a Yamabe almost soliton with a potential collinear to the Reeb vector field. The resulting manifolds are then investigated in two important cases with geometric significance. The first is when the manifold is of Sasaki-like type, i.e. its complex cone is a holomorphic complex Riemannian manifold (also called a K\"ahler--Norden manifold). The second case is when the soliton potential is torse-forming, i.e. it satisfies a certain recurrence condition for its covariant derivative with respect to the Levi-Civita connection of the corresponding metric. The studied solitons are characterized. In the three-dimensional case, an explicit example is constructed and the properties obtained in the theoretical part are confirmed.