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arXiv · 1906.02952

Harmonic symmetries for Hermitian manifolds

Scott O. Wilson
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Abstract

Complex manifolds with compatible metric have a naturally defined subspace of harmonic differential forms that satisfy Serre, Hodge, and conjugation duality, as well as hard Lefschetz duality. This last property follows from a representation of $sl(2,\mathbb{C})$, generalizing the well known structure on the harmonic forms of compact Kähler manifolds. Some topological implications are deduced.

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Scott O. Wilson. 2020-01-16. Harmonic symmetries for Hermitian manifolds. https://arxiv.org/abs/1906.02952

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