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