On non-pure forms on almost complex manifolds

2012/11/10 by Hind, Richard, Medori, Costantino, Tomassini, Adriano
#32Q60 #53C15 #58A12 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1211.2334

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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