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On cohomological decomposability of almost-Kähler structures

Authors: Daniele Angella, Adriano Tomassini and Weiyi Zhang
Journal: Proc. Amer. Math. Soc. 142 (2014), 3615-3630
MSC (2010): Primary 53C55, 53C25, 32G05
Published electronically: July 10, 2014
MathSciNet review: 3238437
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Abstract: We study the $ J$-invariant and $ J$-anti-invariant cohomological subgroups of the de Rham cohomology of a compact manifold $ M$ endowed with an almost-Kähler structure $ \left (J,\,\omega ,\,g\right )$. In particular, almost-Kähler manifolds satisfying a Lefschetz type property and solvmanifolds endowed with left-invariant almost-complex structures are investigated.

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Additional Information

Daniele Angella
Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy

Adriano Tomassini
Affiliation: Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/A, 43124 Parma, Italy

Weiyi Zhang
Affiliation: Department of Mathematics, 1825 East Hall, University of Michigan, Ann Arbor, Michigan 48109

Keywords: $\mathcal{C}^\infty$-pure-and-full structure, $J$-anti-invariant cohomology, almost-K\"ahler structure
Received by editor(s): April 18, 2012
Received by editor(s) in revised form: September 14, 2012, and October 25, 2012
Published electronically: July 10, 2014
Additional Notes: The first and second authors were partially supported by GNSAGA of INdAM
Communicated by: Franc Forstneric
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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