Hodge–Bott–Chern decompositions of mixed type forms on foliated Kähler manifolds
Volume 137 / 2014
Colloquium Mathematicum 137 (2014), 89-102
MSC: Primary 53C12, 57R30; Secondary 55N34, 32C36, 53B40.
DOI: 10.4064/cm137-1-6
Abstract
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.
