We review some properties of two special types of almost complex structures, introduced by T.-J. Li and W. Zhang in [11], in relation to the existence of compatible symplectic structures and to the Hard Lefschetz condition. The two types of almost complex structures are defined respectively in terms of differential forms and currents. The paper is based on the results obtained in [9]. We give a new example of an 8-dimensional compact solvmanifold endowed with a C ∞ pure and full almost complex structure calibrated by a symplectic form satisfying the Hard Lefschetz condition.
On the cohomology of almost complex manifolds
FINO, Anna Maria;
2010-01-01
Abstract
We review some properties of two special types of almost complex structures, introduced by T.-J. Li and W. Zhang in [11], in relation to the existence of compatible symplectic structures and to the Hard Lefschetz condition. The two types of almost complex structures are defined respectively in terms of differential forms and currents. The paper is based on the results obtained in [9]. We give a new example of an 8-dimensional compact solvmanifold endowed with a C ∞ pure and full almost complex structure calibrated by a symplectic form satisfying the Hard Lefschetz condition.
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