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arXiv · 2402.06893

The hard Lefschetz duality for locally conformally almost Kähler manifolds

Shuho Kanda
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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.

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Shuho Kanda. 2024-02-10. The hard Lefschetz duality for locally conformally almost Kähler manifolds. https://doi.org/10.1016/j.difgeo.2025.102239

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