Conformally symplectic structures and the Lefschetz condition

2024/03/18 by Lejmi, Mehdi, Wilson, Scott O.
#Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2403.12304

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.

Related

• The hard Lefschetz duality for locally conformally almost Kähler manifolds
• Darboux-Weinstein theorem for locally conformally symplectic manifolds
• Examples of non d_ω-exact locally conformal symplectic forms
• Formality and the Lefschetz property in symplectic and cosymplectic geometry
• Locally conformally symplectic bundles