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Almost Riemann solitons are introduced and studied on an almost contactcomplex Riemannian manifold, i.e. an almost contact B-metric manifold, obtainedfrom a cosymplectic manifold of the considered type by a contact conformaltransformation of the Reeb vector field, its dual contact 1-form, the B-metric,and its associated B-metric. The potential of the studied soliton is assumed tobe in the vertical distribution, i.e. it is collinear to the Reeb vector field.In this way, manifolds from the four main classes of the studied manifolds areobtained. Curvature properties of the resulting manifolds are derived. Anexplicit example of dimension five is constructed. The Bochner curvature tensoris used (for dimension at least seven) as a conformal invariant to getproperties and construct an explicit example in relation to the obtainedresults.

Almost Riemann Solitons with Vertical Potential on Conformal Cosymplectic Contact Complex Riemannian Manifolds