The hard Lefschetz duality for locally conformally almost Kähler manifolds

2024/02/10 by Kanda, Shuho
#32Q60 #53C55 #53D35 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2402.06893

Abstract

We prove the hard Lefschetz duality for locally conformally almost Kähler manifolds. This is a generalization of that for almost Kähler manifolds studied by Cirici and Wilson. We generalize the Kähler identities to prove the duality. Based on the result, we introduce the hard Lefschetz condition for locally conformally symplectic manifolds. As examples, we give solvmanifolds which do not satisfy the hard Lefschetz condition.

Related

• Conformally symplectic structures and the Lefschetz condition
• Almost Hermitian Identities
• Compatible almost complex structures on the Hard Lefschetz condition
• Darboux-Weinstein theorem for locally conformally symplectic manifolds
• Hard Lefschetz Condition on symplectic non-Kähler solvmanifolds