The hard Lefschetz duality for locally conformally almost K\"{a}hler manifolds
Differential Geometry
2025-06-24 v1 Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.2402.06893,
title = {The hard Lefschetz duality for locally conformally almost K\"{a}hler manifolds},
author = {Shuho Kanda},
journal= {arXiv preprint arXiv:2402.06893},
year = {2025}
}
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14 pages