On non-pure forms on almost complex manifolds

Richard Hind; Costantino Medori; Adriano Tomassini

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arXiv · 1211.2334

On non-pure forms on almost complex manifolds

Richard Hind·Costantino Medori·Adriano Tomassini

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Abstract

T.-J. Li and W. Zhang defined an almost complex structure $J$ on a manifold $X$ to be {\em \Cpf}, 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) that any almost complex structure on a 4-dimensional compact manifold is \Cpf. 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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Richard Hind, Costantino Medori, Adriano Tomassini. 2012-11-10. On non-pure forms on almost complex manifolds. https://arxiv.org/abs/1211.2334

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