On non-pure forms on almost complex manifolds
Symplectic Geometry
2012-11-13 v1
Abstract
T.-J. Li and W. Zhang defined an almost complex structure on a manifold 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 -invariant and -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 -invariant and -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.
Cite
@article{arxiv.1211.2334,
title = {On non-pure forms on almost complex manifolds},
author = {Richard Hind and Costantino Medori and Adriano Tomassini},
journal= {arXiv preprint arXiv:1211.2334},
year = {2012}
}