Abstract
We study a special type of almost complex structures, called pure and full and introduced by T.J. Li and W. Zhang (arXiv:0708.2520, 2007), 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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This work was supported by the Projects MIUR “Riemannian Metrics and Differentiable Manifolds”, “Geometric Properties of Real and Complex Manifolds” and by GNSAGA of INdAM.
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Fino, A., Tomassini, A. On Some Cohomological Properties of Almost Complex Manifolds. J Geom Anal 20, 107–131 (2010). https://doi.org/10.1007/s12220-009-9098-3
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DOI: https://doi.org/10.1007/s12220-009-9098-3
Keywords
- Symplectic structure
- Pure and full almost complex structure
- Calibrated almost complex structure
- Current