Hodge symmetry and decomposition on non-Kähler solvmanifolds

Abstract

Let $G=\C^{n}\ltimes_ϕ \C^{m}$ with a semi-simple action $ϕ: \C^{n}\to GL_{m}(\C)$ (not necessarily holomorphic). Suppose $G$ has a lattice $\Gamma$. Then we show that in 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.

5 pages

References in corpus (2)

• Formality and hard Lefschetz property of aspherical manifolds
• Geometrical formality of solvmanifolds and solvable Lie type geometries