Harmonic symmetries for Hermitian manifolds
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- by Scott O. Wilson
- Proc. Amer. Math. Soc. 148 (2020), 3039-3045
- DOI: https://doi.org/10.1090/proc/14997
- Published electronically: March 18, 2020
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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.References
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Bibliographic 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
- 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
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 3039-3045
- MSC (2010): Primary 53C55
- DOI: https://doi.org/10.1090/proc/14997
- MathSciNet review: 4099790