On some cohomological properties of almost complex manifolds

Details On some cohomological properties of almost complex manifolds On some cohomological properties of almost complex manifolds

2008-11-28

arxiv.org/abs/0811.4765v2

Mathematics

Differential Geometry

19 pages, to be published in Journal Geometric Analysis

Scientific paper

We study a special type of almost complex structures, called pure and full and introduced by T.J. Li and W. Zhang, in relation to symplectic structures and Hard Lefschetz condition. We provide sufficient conditions to the existence of the above type of almost complex structures on compact quotients of Lie groups by discrete subgroups. We obtain families of pure and full almost complex structures on compact nilmanifolds and solvmanifolds. Some of these families are parametrized by real 2-forms which are anti-invariant with respect to the almost complex structures.

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