Conformally symplectic structures and the Lefschetz condition

Abstract

This short note provides a symplectic analogue of Vaisman's theorem in complex geometry. Namely, for any compact symplectic manifold satisfying the hard Lefschetz condition in degree 1, every locally conformally symplectic structure is in fact globally conformally symplectic, whenever there is a mutually compatible almost complex structure.

arXiv commentWithdrawn because implication (1) => (2) in Lemma 2 is false: hard Lefschetz in degree 1 does not imply that J preserves harmonic 1-forms. Consequently, the proofs of Theorem 1 and its dependent corollaries are invalid. This withdrawal does not assert that Theorem 1 itself is false