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Hodge theory for twisted differentials

Daniele Angella, Hisashi Kasuya (2014)

Complex Manifolds

We study cohomologies and Hodge theory for complex manifolds with twisted differentials. In particular, we get another cohomological obstruction for manifolds in class C of Fujiki. We give a Hodgetheoretical proof of the characterization of solvmanifolds in class C of Fujiki, first stated by D. Arapura.

Hodge-Bott-Chern decompositions of mixed type forms on foliated Kähler manifolds

Cristian Ida (2014)

Colloquium Mathematicae

The Bott-Chern cohomology groups and the Bott-Chern Laplacian on differential forms of mixed type on a compact foliated Kähler manifold are defined and studied. Also, a Hodge decomposition theorem of Bott-Chern type for differential forms of mixed type is proved. Finally, the case of projectivized tangent bundle of a complex Finsler manifold is discussed.

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