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Harmonic symmetries for Hermitian manifolds


Author: Scott O. Wilson
Journal: Proc. Amer. Math. Soc. 148 (2020), 3039-3045
MSC (2010): Primary 53C55
DOI: https://doi.org/10.1090/proc/14997
Published electronically: March 18, 2020
MathSciNet review: 4099790
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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 $\mathfrak {sl}(2,\mathbb {C})$, generalizing the well-known structure on the harmonic forms of compact Kähler manifolds. Some topological implications are deduced.


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References
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Additional Information

Scott O. Wilson
Affiliation: Department of Mathematics, Queens College, City University of New York, Flushing, New York 11367
MR Author ID: 812534
Email: scott.wilson@qc.cuny.edu

Keywords: Hermitian manifold, complex manifold, Lefschetz duality
Received by editor(s): June 17, 2019
Published electronically: March 18, 2020
Additional Notes: The author acknowledges support provided by a PSC-CUNY Award, jointly funded by The Professional Staff Congress and The City University of New York
Communicated by: Jia-Ping Wang
Article copyright: © Copyright 2020 American Mathematical Society