On non-pure forms on almost complex manifolds
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- by Richard Hind, Costantino Medori and Adriano Tomassini PDF
- Proc. Amer. Math. Soc. 142 (2014), 3909-3922 Request permission
Abstract:
In 2009 T.-J. Li and W. Zhang defined an almost complex structure $J$ on a manifold $X$ to be $\mathcal {C}^\infty$-pure-and-full if the second de Rham cohomology group can be decomposed as a direct sum of the subgroups whose elements are cohomology classes admitting $J$-invariant and $J$-anti-invariant representatives. It turns out (see T. Draghici, T.-J. Li and W. Zhang (2010)) that any almost complex structure on a $4$-dimensional compact manifold is $\mathcal {C}^\infty$-pure-and-full. We study the $J$-invariant and $J$-anti-invariant cohomology subgroups on almost complex manifolds, possibly non-compact. In particular, we prove an analytic continuation result for anti-invariant forms on almost complex manifolds.References
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Additional Information
- Richard Hind
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- MR Author ID: 623372
- Email: hind.1@nd.edu
- Costantino Medori
- Affiliation: Dipartimento di Matematica e Informatica, Università di Parma, Viale Parco Area delle Scienze 53/A, 43124, Parma, Italy
- Email: costantino.medori@unipr.it
- Adriano Tomassini
- Affiliation: Dipartimento di Matematica e Informatica, Università di Parma, Viale Parco Area delle Scienze 53/A, 43124, Parma, Italy
- MR Author ID: 362161
- Email: adriano.tomassini@unipr.it
- Received by editor(s): August 30, 2011
- Received by editor(s) in revised form: October 12, 2012, and December 14, 2012
- Published electronically: July 22, 2014
- Additional Notes: Partially supported by Fondazione Bruno Kessler-CIRM (Trento) and by GNSAGA of INdAM
- Communicated by: Franc Forstneric
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 3909-3922
- MSC (2010): Primary 32Q60, 53C15, 58A12
- DOI: https://doi.org/10.1090/S0002-9939-2014-11578-4
- MathSciNet review: 3251731