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Motivated by these results, we introduce the notions of a Lefschetz and of a basic Lefschetz locally conformal symplectic l. We prove that the two notions are equivalent if there exists a Riemannian metric such that the Lee vector field is unitary and parallel and its metric dual -form coincides with the Lee -form. Finally, we discuss several examples of compact l. References [Enhancements On Off] What's this? The third author acknowledges the Centre for Mathematics of the University of Coimbra in Portugal for its support and hospitality during a visit where a part of this work was done.

Blair , Riemannian geometry of contact and symplectic manifolds , 2nd ed.

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