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arXiv · 2402.06893

The hard Lefschetz duality for locally conformally almost K\"{a}hler manifolds

Shuho Kanda
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Abstract

We prove the hard Lefschetz duality for locally conformally almost K\"{a}hler manifolds. This is a generalization of that for almost K\"{a}hler manifolds studied by Cirici and Wilson. We generalize the K\"{a}hler 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 K\"{a}hler manifolds. https://doi.org/10.1016/j.difgeo.2025.102239

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