On the geometry of the characteristic vector of an \textit{lcQS}-manifold (Q1946444)

Almost contact metric structures are the odd-dimensional counterpart of almost Hermitian geometry. Among such structures, a special role is played by quasi-Sasakian structures, i.e. normal almost contact metric structures for which the fundamental form is closed. Sasakian and cosymplectic manifolds are particular examples of quasi-Sasakian structures. In the paper under review the authors study locally conformally quasi-Sasakian structures. These are structures that, in a neighborhood of any point, are conformally equivalent to a quasi-Sasakian one. Locally conformally cosymplectic structures are a special case of those. The authors investigate the behaviour of the Reeb vector field on normal locally conformally quasi-Sasakian manifolds. They show that it is torsion-forming if and only if the structure is locally conformal cosymplectic. They show that, in this case, the Reeb vector field is actually concircular. Finally, they give applications to quasi-Sasakian and cosymplectic structures.