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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Harmonic symmetries for Hermitian manifolds
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by Scott O. Wilson PDF
Proc. Amer. Math. Soc. 148 (2020), 3039-3045 Request permission

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
  • J. Cirici and S.O. Wilson, Dolbeault cohomology for almost complex manifolds, Preprint arxiv:1809.1416 (2018).
  • J. Cirici and S.O. Wilson, Topological and geometric aspects of almost Kähler manifolds via harmonic theory, Preprint arxiv:1809.1414 (2018).
  • Jean-Pierre Demailly, Sur l’identité de Bochner-Kodaira-Nakano en géométrie hermitienne, Séminaire d’analyse P. Lelong-P. Dolbeault-H. Skoda, années 1983/1984, Lecture Notes in Math., vol. 1198, Springer, Berlin, 1986, pp. 88–97 (French, with English summary). MR 874763, DOI 10.1007/BFb0077045
  • Phillip A. Griffiths, The extension problem in complex analysis. II. Embeddings with positive normal bundle, Amer. J. Math. 88 (1966), 366–446. MR 206980, DOI 10.2307/2373200
  • Dan Popovici, Degeneration at $E_2$ of certain spectral sequences, Internat. J. Math. 27 (2016), no. 14, 1650111, 31. MR 3593673, DOI 10.1142/S0129167X16501111
  • André Weil, Introduction à l’étude des variétés kählériennes, Publications de l’Institut de Mathématique de l’Université de Nancago, VI. Actualités Sci. Ind. no. 1267, Hermann, Paris, 1958 (French). MR 0111056
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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
  • 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