Abstract
Let N=G/Г be a compact nilmanifold, G a connected, simply connected, nilpotent Lie group with its discrete subgroup Г and Lie algebra \(\mathcal{G}\). Let I* (\(\mathcal{G}\)) denote the invariant differential forms on \(\mathcal{G}\).
If I* (\(\mathcal{G}\)) → H* (\(\mathcal{G}\)) is an injective map, then G is abelian and N is a torus. Furthermore, N has a formal minimal model. If N is an even-dimensional compact nilmanifold, it has a Kähler structure and invariant symplectic structure if and only if I* (\(\mathcal{G}\)) → H* (\(\mathcal{G}\)) is injective.
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Güner, N. Invariant differental forms on compact nilmanifolds. Geom Dedicata 63, 17–23 (1996). https://doi.org/10.1007/BF00181183
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DOI: https://doi.org/10.1007/BF00181183