On the Geometry of the Characteristic Vector of an $\mathit{lcQS}$-Manifold

We study conditions under which the characteristic vector of a normal $\mathit{lcQS}$-manifold is a torsion-forming or even a concircular vector field. We prove that the following assertions are equivalent: an $\mathit{lcQS}$-structure is normal, and its characteristic vector is a torsion-forming vector field; an $\mathit{lcQS}$-structure is normal, and its characteristic vector is a concircular vector field; an $\mathit{lcQS}$-structure is locally conformally cosymplectic and has a closed contact form.