English

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 JJ on a manifold XX 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 JJ-invariant and JJ-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 JJ-invariant and JJ-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.

Keywords

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}
}
R2 v1 2026-06-21T22:36:09.332Z