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Hodge symmetry and decomposition on non-Kähler solvmanifolds. (English) Zbl 1279.22010
Author’s abstract: Let \(G = \mathbb C^n \ltimes_\phi \mathbb C^m\) with a semi-simple action \(\phi : \mathbb C^n \to\mathrm{GL}_m(\mathbb C)\) (not necessarily holomorphic). Suppose that \(G\) has a lattice \(\Gamma\). Then we show that under some conditions on \(G\) and \(\Gamma\), \(G/\Gamma\) admits a Hermitian metric such that the space of harmonic forms satisfies the Hodge symmetry and decomposition. By this result we give many examples of non-Kähler Hermitian solvmanifolds satisfying the Hodge symmetry and decomposition.

22E25 Nilpotent and solvable Lie groups
53C30 Differential geometry of homogeneous manifolds
53C55 Global differential geometry of Hermitian and Kählerian manifolds
Full Text: DOI arXiv
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