On non-pure forms on almost complex manifolds

Hind, Richard; Medori, Costantino; Tomassini, Adriano

doi:10.1090/S0002-9939-2014-11578-4

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.

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