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http://hdl.handle.net/2445/192540
Title: | Topological and geometric aspects of almost Kahler manifolds via harmonic theory |
Author: | Cirici, Joana Wilson, Scott O. |
Keywords: | Varietats complexes Geometria diferencial global Grups simplèctics Complex manifolds Global differential geometry Symplectic groups |
Issue Date: | 9-Jun-2020 |
Publisher: | Springer Nature |
Abstract: | The well-known Kähler identities naturally extend to the non-integrable setting. This paper deduces several geometric and topological consequences of these extended identities for compact almost Kähler manifolds. Among these are identities of various Laplacians, generalized Hodge and Serre dualities, a generalized hard Lefschetz duality, and a Lefschetz decomposition, all on the space of $d$-harmonic forms of pure bidegree. There is also a generalization of Hodge Index Theorem for compact almost Kähler 4-manifolds. In particular, these provide topological bounds on the dimension of the space of d-harmonic forms of pure bidegree, as well as several new obstructions to the existence of a symplectic form compatible with a given almost complex structure. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1007/s00029-020-00568-4 |
It is part of: | Selecta Mathematica-New Series, 2020, vol. 26, num. 3 |
URI: | http://hdl.handle.net/2445/192540 |
Related resource: | https://doi.org/10.1007/s00029-020-00568-4 |
ISSN: | 1022-1824 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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706117.pdf | 277.1 kB | Adobe PDF | View/Open |
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